Hastings' Dictionary of the New Testament 
Under this term students of the Greek Testament have to do with only one word—and that a verb, αὐξάνω. The consideration of the corresponding substantive does not properly form the subject of inquiry in this Dictionary. Rare in classical literature, αὔξησις is used only twice in the NT, viz. in Ephesians 4:16 and Colossians 2:19. The verb is, however, employed some twelve times within the four Gospels. It is a verb of exceedingly doubtful derivation, but probably is etymologically linked with the German wachsen and our own wax ; less certainly with the Latin augeo . Its underlying meaning is that of additional size, bulk, or power. The normal usage of the verb in the Classics implies that such access comes from without, it is superimposed by some external agency. This significance lies both in the transitive and intransitive use of the verb, and affords, as will be seen, a striking contrast with its use in the Greek Testament. Quotations are not needful. The verb is employed by classical writers from Homer downwards to mark efforts to increase the power of the State or of a country, of special honour paid to parents, of the exaggerations of orators, of the waxing of the moon, of the noontide heat of the sun, of the height of the waves of the sea. Enough to say that in classical literature the verb marks an increase or addition to a person or thing brought about by external agency.
The Hebrew language is very rich in terms which signify ‘growth.’ There are some 16 words, verbs and nouns substantive, which bear this general meaning. It is enough to say here that they are capable of a single classification. One set of expressions corresponds to αὑξάνω in the sense already indicated; the other, which is preponderant, marks ‘growth’ of the physical order, seminal growth; and is applied with a great wealth of illustration to the life of plants, trees, the brute creation, and of man himself. Every student of the Psalter or of the Prophetical books is aware of the word-pictures here in which the writers take delight, a delight which is spiritual more than intellectual, of the heart rather than the mind. The natural laws of physical development are by these writers boldly made to apply to the spiritual world. Jehovah, supreme in the one sphere, is supreme in the other. Growth is from within, but yet it is ‘God who giveth the increase.’
When the student turns to the NT, and to the idea of growth which finds expression there, he finds that there is a greater affinity of conception between the inspired writers of both Testaments than there is between the writers of the NT and classical Greek writers. The affinity simply lies in the common conception, with its spiritual applications, of a germinal growth, expanding and blossoming unto fruitage whether in nature or in grace.
1. References in the Gospels .—With the above preliminaries, the issue may now be considered in relation to the four Gospels. And first, the less careful student must be warned that the quotation which records the pathetic plea of the disciples to their Lord, ‘Increase our faith,’* [Note: Luke 17:5πρόσθες ἡμῖν τίστιν.] stands out as an exception. The translation [Authorized Version and Revised Version NT 1881, OT 1885] may serve, but it is doubtful whether ‘our’ is admissible. Despite the verb, it is questionable whether the disciples then asked for a growth of that spirit of which they were consciously possessed. Were they not rather asking for some gift new and strange to their experience? In any case growth of the physical order is not in place here; for this we must look, as has been shown, almost exclusively to the verb αὐξάνω. This verb is of frequent occurrence in the Gospels, although only once employed by the Fourth Evangelist,† [Note: John 3:30 opposed to ἐλαττοῦσθαι.] when the Baptist’s language is rendered as expressing the growing authority of the new Teacher, and the increasing number of His adherents. It is interesting to observe that with regard to all other instances of the occurrence of this word, they either apply, as here, to the Lord Himself, or else form a part of His own utterances; nor is the interest of the point largely affected by the admission that our Lord would normally use Aramaic. The Evangelists doubtless discovered in the verb αὐξάνω what they wished to convey about His childhood, and what they understood Him to teach in lessons drawn from the natural world.
In his unique account of our Lord’s childhood the Second Evangelist declares of Him ( Luke 2:40) that which he had in precisely the same terms declared of the Baptist ( Luke 1:80), that ‘the child grew and waxed strong, filled with wisdom’[of the Baptist, ‘in spirit’]; that is, the development of Christ, both spiritually and physically, was normal and equable in its character. The phraseology of St. Luke suggests a contrast with the Apocryphal Gospels, whose account of Christ’s infancy makes Him appear a wonder-working prodigy, a phenomenal child, anxious for the display of supernatural powers. St. Luke will have none of this. He is not content with a single protest, for later ( Luke 2:52) he solemnly declares that as the child Jesus advanced in years so He developed in wisdom and in favour with God and men. Here, however, the ‘growth’ is not explicitly stated, the rare verb (προέκοπτεν) used marking rather advancement, or progress triumphing over difficulties in the way.
The remaining instances of the verb αὐξάνω appear for the most part in our Lord’s parabolic discourses. Thus it is seen to be the characteristic feature of the seed sown.‡ [Note: Mark 4:8, cf. v. 27 where growth is expressed by μηκύνηται.] There is a process of secret assimilation between it and the good ground; and growth, not sterility or a rash prematurity, is the consequence.§ [Note: The lessons as to hindrances to growth taught in the Parable of the Sower would need a separate study.] In the immortal contrast ( Matthew 6:28, cf. Luke 12:27) between the lilies of the field and the garish splendour of Solomon’s court dress, it is less upon the beauty of the flowers that Christ lays stress than upon their growth, gradual and all unconscious, spontaneous, effortless. In the parable of the Tares and Wheat this characteristic verb appears in the permission, at once generous and awful, of the master to his servants to let both grow together until the harvest ( Matthew 13:30). In the same parabolic discourse it is the growth of the mustard-seed, the development of the surprisingly little, which furnishes an analogue of the spread of the Church universal ( Matthew 13:31). Lastly, although we have not here the verb αὐξάνω, we find the mysterious condemnation passed upon the barren fig-tree ( Matthew 21:19), a condemnation of that which is purely physical, sterility in fruit, which fruit in the world of men as in the life of plants and trees is the consequence of all true growth.
2. The underlying idea .—It seems somewhat strange, since the OT is so full of religious teaching drawn from physical growth, that only in the one instance, quoted above, of our Lord’s childhood is a spiritual application of the idea directly made in the Gospel narrative. Christ, we may reverently say it, was content to lay the conception which was ever before Him, in garden, harvest field, and orchard, also before His own. If they had eyes to see these things, and ears to hear them,—if they would only ‘consider’ ( Luke 12:24; Luke 12:27) them,—heart and conscience would do the rest. Then they, as we, would perceive this natural law in the spiritual world—a growing within, secret, beautiful, fertile, in men, and yet not of man, yielding the increase and harvest of the Spirit, His fruit rather than their works.
3. Application of the idea .—But if it is thought even by devout and careful students that such ideas are more than may be gathered from our Lord’s actual utterances, those who treasured His sayings in the Apostolic age did not think so. St. Peter and St. Paul no longer use the idea of growing as a metaphor. It is a gracious fact both for the Church and the individual believer. Thus the Apostle of the Gentiles uses the conception of inward Christian growth ( Ephesians 4:15), and so as to form a shrine wherein the Divine presence may be manifest ( Ephesians 2:21); his prayer for his Colossian converts is that they may grow in further knowledge of God ( Colossians 1:10); his promise to them if they ‘hold the Head’ ( Colossians 2:19), is that they shall grow with a Divine increase. Twice he assures the Corinthians ( 1 Corinthians 3:8) that this growth, although in them, has a Divine origin. St. Peter ( 1 Peter 2:2, cf. [ 2 Peter 3:18]) shows that the Holy Scriptures have their own function in the growth of grace. It is enough; the conception is carried through from one Testament to the other, and its teaching is consecrated, its consolation is secured in and through Him whom the great Evangelical prophet ( Isaiah 11:1) prefigured as the very symbol of growing: ‘There shall come forth a shoot out of the stock of Jesse, and a branch out of his roots shall bear fruit,’ That fruit is still seen in every plant planted by the Divine Husbandman ( Matthew 15:13).
King James Dictionary 
GROWING, ppr. Increasing advancing in size or extent becoming accruing swelling thriving.