King James Dictionary 
ASI'DE, ad. a and side. See Side.
1. On or to one side out of a perpendicular or straight direction. 2. At a little distance from the main part or body.
Thou shalt set aside that which is full. 2 Kings 4 .
3. From the body as, to put or lay aside a garment.
John 13 .
4. From the company at a small distance or in private as when speakers utter something by themselves, upon the stage. 5. Separate from the person, mind or attention in a state of abandonment.
Let us lay aside every weight. Hebrews 12 .
6. Out of the line of rectitude or propriety, in a moral view.
They are all gone aside. Psalms 14 .
7. In a state of separation to a particular use as, to set aside a thing for a future day.
To set aside, in judicial proceedings, is to defeat the effect or operation of, by a subsequent decision of a superior tribunal as, to set aside a verdict or a judgment.
Webster's Dictionary 
(1): (adv.) On, or to, one side; out of a straight line, course, or direction; at a little distance from the rest; out of the way; apart.
(2): (adv.) Out of one's thoughts; off; away; as, to put aside gloomy thoughts.
(3): (adv.) So as to be heard by others; privately.
(4): (n.) Something spoken aside; as, a remark made by a stageplayer which the other players are not supposed to hear.
Vine's Expository Dictionary of NT Words 
International Standard Bible Encyclopedia 
a - sı̄d ´: "Distinct from others," "privately," such is the sense of the word in 2 Kings 4:4; Mark 7:33 . Also "to withdraw" ( Luke 9:10 the King James Version; Acts 23:19 : ὑποχωρέω , hupochōréō , also anachoréō ). One is said to have turned aside when he departs from the path of rectitude ( Psalm 14:3; Sirach 2:7; 1 Timothy 1:6 ). In a figurative sense it is used to express the thought of putting aside, to renounce, every hindrance or impediment to a consecrated earnest Christian life ( Hebrews 12:1 : ἀποτίθημι , apotı́thēmi ).