Hastings' Dictionary of the New Testament 
The English word ‘abound’ in the Epistles of the NT is the translation of the Gr. words πλεονάζω and περισσεύω. There is nothing of special interest in these terms; perhaps the former has the less lofty sense, its primary connotation being that of superfluity. As used by St. Paul, however, there seems little to choose between them, although it is worth noting that, where he speaks ( Romans 5:20) of the ‘offence’ and ‘sin’ abounding, he uses πλεονάζειν. Yet he employs the same term in Romans 6:1 of the ‘abounding of grace,’ and in Philippians 4:17 of the fruit of Christian giving. His favourite term, however, is περισσεύω (in one case ὑπερπερισσεύω, ‘overflow,’ Romans 5:20), whether he is speaking of the grace of God ( Romans 5:15), the sufferings of Christ ( 2 Corinthians 1:5), or the Christian spirit that finds expression in liberality ( 2 Corinthians 8:7; 2 Corinthians 9:8), contentment ( Philippians 4:12; Philippians 4:18), hope ( Romans 5:15), service ( 1 Corinthians 15:58). This list of references is not exhaustive, but it is representative. These words and the way in which they are used give us a suggestive glimpse into-
1. The religious temperament of the Apostle. -His was a rich and overflowing nature, close-packed with vivid, ever-active qualities of mind and heart. His conception of the gospel would be naturally in accordance with the wealth of his psychic and moral nature; he would inevitably fasten on such aspects of it as most thoroughly satisfied his own soul; and he would put its resources to the full test of his spiritual needs and capacities. It is fortunate that Christianity found at its inception such a man ready to hand as its chief exponent to the primitive churches, and that his letters remain as a record of the marvellous way in which he opened his heart to its appeal, and of the manifold response he was able to make to that appeal. In all ages our faith has been conditioned by the human medium in which it has had to work. The ages of barrenness in Christian experience have been those which have lacked richly-endowed personalities for its embodiment and exposition; and vice versa , when such personalities have arisen and have given themselves wholeheartedly to the Divine Spirit, there has been a wide-spread efflorescence of religious experience in the Church at large. Ordinary men and women are pensioners religiously, to a peculiar degree, of the great souls in the community. St. Paul, Origen, Augustine, Bernard, Luther, Wesley, etc., have been the focal points through which the forces of the gospel have radiated into the world at large, and lifted its life to higher levels.
2. The superabundant wealth of the gospel as a medium of the Divine energies of redemption. -The Christian faith is full of spiritual resources on which the soul may draw to the utmost of its needs. In the teaching of our Lord, the prodigality of His illustrations, their varied character, and the frequency with which He likens the Kingdom to a ‘feast,’ with all its suggestions of a large welcome and an overflowing abundance of good things, are very characteristic of His own attitude towards the gospel He preached; and St. Paul is preeminent among NT writers for the way in which he has grasped the same idea, and caught the spirit of the Master in his exposition of spiritual realities. (Cf. ‘How many hired servants of my father’s have bread enough and to spare’ [ Luke 15:17] with ‘the grace of God, which is by one man, Jesus Christ, hath abounded unto many’ [ Romans 5:15; also Romans 5:17; Romans 5:19-21], and many other passages.)
3. The call for an adequate response on the part of believers to the varied and abundant resources of the gospel. -Here, again, St. Paul exhausts the power of language in urging his converts to allow the Divine energies of salvation to have their way with them. The normal type of Christian is not reached till his nature is flooded with the grace of God, and he in turn is lifted into a condition which is characterized by an abounding increase of hope, grace, love, good works, and fruitfulness of character. ‘Therefore, as ye abound in (everything), see that ye abound in this grace also’ ( 2 Corinthians 8:7) expresses one of his favourite forms of appeal. He was not satisfied to see men raised to a slightly higher plane by their faith in Christ; they were to be ‘transformed in the spirit of their minds’ ( Romans 12:2); they were always to ‘abound in the work of the Lord’ ( 1 Corinthians 15:58; cf. 2 Corinthians 9:8); and, as ‘they had received’ of him how they might walk and ‘to please God,’ they were exhorted to ‘abound more and more’ ( 1 Thessalonians 4:1), and that especially because they knew what commandments ‘had been given them by the Lord Jesus’ ( 1 Thessalonians 4:2). It was a subject for joyfulness to him when he found his converts thus responding to the power of God (see 2 Corinthians 8:1 f.). As regards his realization of this Divine abundance in his own experience, we find him breaking out into an ecstasy of thanksgiving at the thought of what God has done for him, and of the sense of inward spiritual abundance which he consequently enjoys, so that he feels quite independent of all outward conditions, however hard they may be (cf. Philippians 4:11-13). This is the language of a man who enjoys all the resources of the God-head in his inner life, and who can, therefore, be careless of poverty, misfortune, sickness, and even the prospect of an untimely end.
Literature.-See Sanday-Headlam, and Lightfoot (especially Notes on Epistles of St. Paul ), on the passages referred to, also Phillips Brooks, The Light of the World , 1891, p. 140, and Expository Times viii.  514a.
King James Dictionary 
ABOUND'ING, ppr. Having in great plenty being in great plenty, being very prevalent generally prevailing.
ABOUND'ING, n. Increase.
Webster's Dictionary 
(p. pr. & vb. n.) of Abound