Vine's Expository Dictionary of OT Words 
Zâkar ( זָכַר , Strong'S #2142), “to remember, think of, mention.” This root is found in Assyrian, Aramaic, Arabic, and Ethiopic. The group of words (the verb and the three nouns derived from it) is found throughout the Old Testament. The first occurrence of zâkar is in Gen. 8:1 with God as the subject: “God remembered Noah … : and God made a wind to pass over the earth, and the waters assuaged.” In Gen. 9:15 God said to Noah: “And I will remember my covenant …; and the waters shall no more become a flood to destroy all flesh.” As in these two cases (cf. Gen. 6:18), “remember” is used of God in respect to His covenant promises and is followed by an action to fulfill His covenant. God delivered Lot from Sodom because of His covenant with Abraham to bless all the nations through him (Gen. 18:17-33): “God remembered Abraham, and brought Lot out of the catastrophe …” (Gen. 19:29, NIV). This marks the history of Israel at every major point: “And I have also heard the groaning of the children of Israel, … and I have remembered my covenant.… and I will bring you out from under the burdens of the Egyptians …” (Exod. 6:5-6). The promise “to remember” was repeated in the covenant at Sinai (Lev. 26:40-45), God’s remembrance was sung in the Psalms (98:3; 105:8, 42; 106:45), and the promise was repeated by the prophets in regard to restoration from captivity (Ezek. 16:60). The new covenant promise is: “… I will forgive their iniquity, and I will remember their sin no more” (Jer. 31:34).
Because of this God’s people pray, as Moses: “Turn from thy fierce wrath.… Remember Abraham, Isaac, and Israel, thy servants, to whom thou swarest …” (Exod. 32:12-13); or Nehemiah: “Remember … the word that thou commandedst thy servant Moses …” (Neh. 1:8, quoting Lev. 26:33); or the psalmist: “Remember not the sins of my youth, nor my transgressions: according to thy mercy remember thou me …” (Ps. 25:7); or Jeremiah: “… Remember, break not thy covenant with us” (Jer. 14:21).
Men also “remember.” Joseph said to Pharaoh’s butler: “But think on me … , and make mention of me unto Pharaoh …” (Gen. 40:14; NIV, “remember … and mention”). Again, “to remember” means more than “to recall”; it means “to retain in thought” so as to tell someone who can take action (cf. Ps. 20:7). Zâkar may have more specific connotations in certain circumstances: “Hear ye this, O house of Jacob, … which swear by the name of the Lord, … and make mention of the God of Israel …” (Isa. 48:1). The NASB and the NIV translate the last clause “and invoke the God of Israel”; and the RSV has “confess.” All point to the mention of God’s name in worship. David appointed “Levites as ministers before the ark of the Lord, to invoke … the Lord …” (1 Chron. 16:4, Rsv; Nasb “to celebrate”; NIV, “to make petition”).
The covenant commanded Israel to “remember this day, in which ye came out from Egypt …” (Exod. 13:3); to “remember the sabbath day …” (Exod. 20:8); to “remember that thou wast a servant in the land of Egypt, and that the Lord thy God brought thee out thence through a mighty hand …” (Deut. 5:15 and often); and to “remember his marvelous works …” (Ps. 105:5; cf. 1 Chron. 16:15). But “the children of Israel remembered not the Lord their God, who had delivered them out of the hands of all their enemies …” (Judg. 8:34; cf. Ps. 78:42).
Zêker ( זֶֶכֶר , Strong'S #2143), or Zeker ( זֶֶכֶר , Strong'S #2143), “remembrance; memorial.” Of His covenant name, 'BCB (“Lord”), God said: “… This is my memorial unto all generations” (Exod. 3:15; cf. Ps. 30:4; 135:13). The name would recall His acts of covenant fulfillment. Moses was told to write an account of the war with Amalek “for a memorial [ zikkaron ] in a book, and rehearse it in the ears of Joshua: for I will utterly put out the remembrance [ zeker ] of Amalek from under heaven” (Exod. 17:14).
The noun zikkaron has similar meanings. God gave the bronze plates covering the altar (Num. 16:40) and the heap of stones at the Jordan (Josh. 4:7, 20-24) as perpetual “memorials” for the sons of Israel. The names of the twelve tribes of Israel were engraved on two stones that were attached to the ephod as “stones of memorial unto the children of Israel: and Aaron shall bear their names before the Lord …” (Exod. 28:12; cf. v. 29). When Israel went into battle, and when they offered sacrifice, they were to blow trumpets “that they may be to you for a memorial before your God” (Num. 10:9-10).
The noun ‘azkarah means “memorial offering” and it occurs primarily in Leviticus. “Memorials” were directed toward God. A “memorial” portion of each meal offering was burnt on the altar (Lev. 2:2, 9, 16), in other words a small portion in place of the whole amount.
The Septuagint translates these words by several derivatives from one root, mimnesko , by which the idea comes into the New Testament. Zechariah praised the Lord God that He had “raised up a horn of salvation for us in the house of his servant David … and to remember his holy covenant …” (Luke 1:69-73). Our need for a reminder is met in “This do in remembrance of me” (1 Cor. 11:24-25).
King James Dictionary 
REMEM'BER, Low L. rememoror re and memoror. See Memory.
1. To have in the mind an idea which had been in the mind before, and which recurs to the mind without effort.
We are said to remember any thing, when the idea of it arises in the mind with the consciousness that we have had this idea before.
2. When we use effort to recall an idea, we are said to recollect it. This distinction is not always observed. Hence remember is often used as synonymous with recollect, that is, to call to mind. We say, we cannot remember a fact, when we mean, we cannot recollect it.
Remember the days of old. Deuteronomy 32 .
3. To bear or keep in mind to attend to.
Remember what I warn thee shun to taste.
4. To preserve the memory of to preserve from being forgotten.
Let them have their wages duly paid, and something over to remember me.
5. To mention. Not in use. 6. To put in mind to remind as, to remember one of his duty. Not in use. 7. To think of and consider to meditate. Psalms 63 . 8. To bear in mind with esteem or to reward. Ecclesiastes 9 . 9. To bear in mind with praise or admiration to celebrate. 1 Chronicles 16 . 10. To bear in mind with favor, care, and regard for the safety or deliverance of any one. Psalms 74 . Genesis 8 . Genesis 19 . 11. To bear in mind with intent to reward or punish.
3 John 1:10 . Jeremiah 31 .
12. To bear in mind with confidence to trust in. Psalms 20 . 13. To bear in mind with the purpose of assisting or relieving. Galatians 2 . 14. To bear in mind with reverence to obey.
Remember thy Creator in the days of thy youth. Ecclesiastes 12 .
15. To bear in mind with regard to keep as sacred to observe.
Remember the sabbath day, to keep it holy. Exodus 20 .
To remember mercy, is to exercise it. Habakkuk 3 .
Webster's Dictionary 
(1): ( v. i.) To execise or have the power of memory; as, some remember better than others.
(2): ( v. t.) To put in mind; to remind; - also used reflexively and impersonally.
(3): ( v. t.) To mention.
(4): ( v. t.) To recall to the mind of another, as in the friendly messages, remember me to him, he wishes to be remembered to you, etc.
(5): ( v. t.) To be capable of recalling when required; to keep in mind; to be continually aware or thoughtful of; to preserve fresh in the memory; to attend to; to think of with gratitude, affection, respect, or any other emotion.
(6): ( v. t.) To have ( a notion or idea) come into the mind again, as previously perceived, known, or felt; to have a renewed apprehension of; to bring to mind again; to think of again; to recollect; as, I remember the fact; he remembers the events of his childhood; I cannot remember dates.