From BiblePortal Wikipedia

Vine's Expository Dictionary of NT Words [1]

1: Μελετάω (Strong'S #3191 — Verb — meletao — mel-et-ah'-o )

primarily, "to care for" (akin to melete, "care;" cp. melei, "it is a care"), denotes (a) "to attend to, practice,"  1—Timothy 4:15 , RV, "be diligent in" (AV, "meditate upon"); to practice is the prevalent sense of the word, and the context is not against this significance in the RV rendering; some mss. have it in  Mark 13:11; (b) "to ponder, imagine,"  Acts 4:25 . See Imagine.

2: Προμελετάω (Strong'S #4304 — Verb — promeletao — prom-el-et-ah'-o )

"to premediate," is used in  Luke 21:14 .

 Mark 13:11

Vine's Expository Dictionary of OT Words [2]

Hâgâh ( הָגָה , Strong'S #1897), “to meditate, moan, growl, utter, speak.” This word is common to both ancient and modern Hebrew. Found only 25 times in the Hebrew Old Testament, it seems to be an onomatopoetic term, reflecting the sighing and low sounds one may make while musing, at least as the ancients practiced it. This meaning is seen in its first occurrence in the text: “This book of the law shall not depart out of thy mouth; but thou shalt meditate therein day and night …” (Josh. 1:8). Perhaps the most famous reference “to meditating” on the law day and night is Ps. 1:2.

Hâgâh also expresses the “growl” of lions (Isa. 31:4) and the “mourning” of doves (Isa. 38:14). When the word is used in the sense of “to mourn,” it apparently emphasizes the sorrowful sounds of mourning, as seen in this parallelism: “Therefore will I howl for Moab, and I will cry out for all Moab; mine heart shall mourn for the men of Kir-heres” (Jer. 48:31). The idea that mental exercise, planning, often is accompanied by low talking seems to be reflected by Prov. 24:1-2: “Be not thou envious against evil men, … for their heart studieth destruction, and their lips talk of mischief.”

King James Dictionary [3]

Med'Itate, L meditor.

1. To dwell on any thing in thought to contemplate to study to turn or revolve any subject in the mind appropriately but not exclusively used of pious contemplation, or a consideration of the great truths of religion.

His delight is in the law of the Lord, and in his law doth he meditate day and night.  Psalms 1

2. To intend to have in contemplation.

I meditate to pass the remainder of life in a state of undisturbed repose.

MED'ITATE, To plan by revolving in the mind to contrive to intend.

Some affirmed that I meditated a war.

1. To think on to revolve in the mind.

Blessed is the man that doth meditate good things.

Webster's Dictionary [4]

(1): ( v. i.) To keep the mind in a state of contemplation; to dwell on anything in thought; to think seriously; to muse; to cogitate; to reflect.

(2): ( v. t.) To contemplate; to keep the mind fixed upon; to study.

(3): ( v. t.) To purpose; to intend; to design; to plan by revolving in the mind; as, to meditate a war.