Hastings' Dictionary of the New Testament 
(lit.[Note: literally, literature.]‘one-foldedness’)
(a) In Romans 16:18 the term ‘simple’ is used in the Authorized Versionto translate ἄκακος. False teachers by smooth and fair speech beguile the hearts of the ‘simple.’ These are inexperienced Christians, unfamiliar with the duplicity of guile, ἄκακος in Hebrews 7:26 is used in the purely good sense, of ‘guileless,’ and is applied to Jesus, but here the word seems to be used in a slightly derogatory sense-so ignorant of evil as to be easily deceived by evil.
(b) In Romans 16:19 the word ‘simple,’ translating ἀκέραιος (lit.[Note: literally, literature.]‘free from foreign admixture,’ as, e.g., wine unmingled with water, unalloyed metal), has no such derogatory significance. St. Paul would have his readers innocent without being ignorant; discerning the wiles of Satan, yet without sin-craft: in wisdom many-sided-in aim and affection single-minded (cf. 1 Corinthians 14:20, ‘Be not children in mind: howbeit in malice, be ye babes’).
(c) In 1 Peter 2:2 ἄδολος is used in the sense of ‘simple,’ ‘unadulterated’: ‘Desire the sincere milk of the word’ (Authorized Version: the word ‘sincere’ being used in its early English sense of ‘unmixed’). See R. C. Trench Synonyms of the NT8, London, 1876 p. lvi.
(d) ‘Simplicity’ is given as the Authorized Versiontranslation of ἁπλότης in Romans 12:8 : ‘He that giveth, let him do it with simplicity.’ The Greek word indicates one-foldedness; in regard to giving, the term suggests that there is no two-sidedness in the act, that the impulse to help is not checked by a spirit of grudging selfishness. Thus the sense of ‘liberality’ became attached to the word, and so it is translated in the Revised Versionof this passage (cf. 2 Corinthians 8:2 [Authorized Versionand Revised Version] 2 Corinthians 9:11; 2 Corinthians 9:13, James 1:5).
In 2 Corinthians 11:3 St. Paul fears lest the church at Corinth, like tempted Eve, ‘should be corrupted from the simplicity (both Authorized Versionand Revised Version) that is toward Christ.’ The noun (ἁπλότης) would be better translated here ‘singleness of heart,’ as in Authorized Versionand Revised Versionof Ephesians 6:5 and Colossians 3:22 (‘Obey your masters in singleness of heart,’ i.e. in contrast to the double-deal ingot eye-service). In Acts 2:46 (‘They’-i.e. the members of the primitive Church-‘did take their food with gladness and singleness of heart’) the same idea is expressed by another phrase-ἀφελότητι καρδίας-the figure suggested being that of a field clear of stony ground (ἀ + φελλεύς). The Authorized Versiontranslation‘simplicity’ of 2 Corinthians 1:12 rests on an inferior reading-ἁπλότηι for ἁγιότητι.
Hastings' Dictionary of the Bible 
1 . In the OT ‘simple’ is, with one exception, the translation of a word ( pÄ•thÃ® ), whose root-idea is ‘openness.’ Openness of mind is praiseworthy when it implies willingness to receive instruction; it becomes blameworthy when it connotes a disposition equally receptive of good and of evil, or an incapacity to distinguish between right and wrong. In Proverbs ‘the simple’ are represented as needing ‘prudence’ ( Proverbs 1:4 RVm [Note: Revised Version margin.] ), and they are exhorted to ‘understand prudence’ ( Proverbs 8:5 RVm [Note: Revised Version margin.] ). In Proverbs 14:15; Proverbs 14:18 ‘the prudent’ are favourably contrasted with ‘the simple’ who ‘believe every word,’ and therefore ‘inherit folly.’ It is ‘the testimony of the Lord’ that makes the simple wise ( Psalms 19:7; cf. Psalms 119:130 ). In 2 Samuel 15:11 ‘simplicity’ means ‘integrity’ ( tÃ´m ). In the LXX [Note: Septuagint.] the Heb. word ( yÃ´sher ) for ‘straightness’ or ‘uprightness’ is translated by the NT equivalent of ‘simplicity’ ( haplotÃ§s ).
2 . In the NT ‘simple’ ( akeraios = Lat. integer ) is used twice ( Matthew 10:16 RVm [Note: Revised Version margin.] , Romans 16:19 ) to describe the character in which there is ‘no foreign admixture’; the RV [Note: Revised Version.] retains ‘simplicity’ as the rendering of haplotÃ§s only in 2 Corinthians 11:3 , where it denotes those in whose character there are ‘no folds,’ who are whole-hearted in their devotion to Christ (Trench, NT Synonyms , Â§ lvi.). The Christian ideal is ‘simplicity toward Christ’ ( 2 Corinthians 11:3 ). In the life of His loyal disciples dove-like simplicity is blended with the wisdom of the serpent ( Matthew 10:16 ). Their ‘eye’ being ‘single’ ( haplous ), their ‘whole body’ is ‘full of light’ ( Matthew 6:22 ). Christ Jesus being made unto them ‘wisdom from God’ ( 1 Corinthians 1:30 ), they are no longer beguiled like Eve, but are ‘wise unto that which is good, and simple unto that which is evil’ ( Romans 16:19 ).
J. G. Tasker.
Webster's Dictionary 
(1): ( n.) The quality or state of being not complex, or of consisting of few parts; as, the simplicity of a machine.
(2): ( n.) Artlessness of mind; freedom from cunning or duplicity; lack of acuteness and sagacity.
(3): ( n.) Freedom from artificial ornament, pretentious style, or luxury; plainness; as, simplicity of dress, of style, or of language; simplicity of diet; simplicity of life.
(4): ( n.) Freedom from subtlety or abstruseness; clearness; as, the simplicity of a doctrine; the simplicity of an explanation or a demonstration.
(5): ( n.) The quality or state of being simple, unmixed, or uncompounded; as, the simplicity of metals or of earths.
(6): ( n.) Weakness of intellect; silliness; folly.
King James Dictionary 
SIMPLIC'ITY, n. L. simplicitas.
1. Singleness the state of being unmixed or uncompounded as the simplicity of metals or of earths. 2. The state of being not complex, or of consisting of few parts as the simplicity of a machine. 3. Artlessness of mind freedom from a propensity to cunning or stratagem freedom from duplicity sincerity. Marquis Dorset, a man for his harmless simplicity neither misliked nor much regarded. 4. Plainness freedom from artificial ornament as the simplicity of a dress, of style, of language, &c. Simplicity in writing is the first or excellences. 5. Plainness freedom from subtilty or abstruseness as the simplicity of scriptural doctrines or truth. 6. Weakness of intellect silliness. Godly simplicity, in Scriptures, is a fair open profession and practice of evangelical truth, with a single view to obedience and to the glory of God.
International Standard Bible Encyclopedia 
sim - plis´i - ti ( פּתיּוּת , pethayyūth ; ἁπλότης , haplótēs ): The words in the Old Testament commonly translated "simplicity" are pethı̄ , "simple" ( Proverbs 1:22 ), pethayyūth , "simplicity" ( Romans 9:13 margin), tōm , "completeness," "integrity" ( 2 Samuel 15:11 ), "They went in their simplicity." In the New Testament, haplotēs , "singleness of mind," "simplicity," occurs in Romans 12:8 , "He that giveth let him do it with simplicity," the Revised Version (British and American) "liberality," margin "Greek: 'singleness'"; 2 Corinthians 1:12 , "in simplicit and godly sincerity," the Revised Version (British and American) (with corrected text) "in holiness and sincerity of God"; 2 Corinthians 11:3 , "the simplicity that is in Christ," the Revised Version (British and American) (with corrected text) "the simplicity and the purity that is toward Christ"; compare Ephesians 6:5; Colossians 3:22 , where the translation is "singleness" In The Wisdom of Solomon 1:1 we have, "Think ye of the Lord with a good mind (the King James Version "heart"), and in singleness (the King James Version "simplicity") of heart seek ye him" ( haplotēs ). our Lord also speaks ( Matthew 6:22; Luke 11:34 ) of the " single eye" ( haploús ), and James ( James 1:5 ) applies haplṓs , "simply," "directly," without after-thought (the King James Version and the Revised Version (British and American) "liberally") to God, who had been described by Plato ( Rep . ii. 382 E ) as being perfectly simple ( haplous ) and true, both in word and deed. In such "simplicity" - openness, sincerity, freedom from double-mindedness - man most resembles God and is most open to His visitation and blessing.