We are forced to use human terms and categories to describe the God of Israel. We call this anthropomorphic language. The Hebrew word zākar is often used to speak of God remembering His covenant with His people (Gen. 9:15-16; Exod. 6:5; Lev. 26:42, 45; Ps. 105:8, 42; 106:45). Exodus 2:24 says that as a when God heard “their groaning in Egypt,” He “remembered his covenant with Abraham, with Isaac, and with Jacob.”
The word zākar also appears in prayers recorded in the Bible by people like Moses (Exod. 32:13), Samson (Judges 16:28), Hezekiah (2 Kings 20:3), Nehemiah (Neh. 13:14, 22, 29, 31), Jeremiah (Jer.15:15; Lam. 5:1), and Habakkuk (Hab. 3:2). These prayers are calling on God to more than know about them or the statements in His covenants. They are a call for God to act on their behalf.
There are three groups of meanings [for zākar]: 1) for completely inward mental acts such as “remembering” or “paying attention to,” 2) for such inward mental acts accompanied by appropriate external acts, and 3) for forms of audible speaking with such meanings as “recite” or “invoke.” … This range of meanings shows the same blending or overlapping between mental states and external acts seen also in other Hebrew terms (e.g. Hebrew šāmaʿ “to hear”).
Other scriptures instruct the people to remember God or His commandments (Deut. 8:18; Joshua 1:13; Eccl.12:1; Mal. 4:4). These passages are not commands to prepare for a history quiz. They are a call for them to do what God has commanded.
We often you the expression is a similar way when we tell someone to remember to do something. The expectation is that action will follow. When God “remembers” His covenant, it means that he is going to act to fulfill His promises.
 Bob Utley, The Exodus of Israel from Egypt: God Fulfills His Promise to Abraham (Bible Lessons International, 2014), p 27 < http://www.freebiblecommentary.org/old_testament_studies/VOL02OT/VOL02OT.pdf>
 R. Laird Harris, Gleason L. Archer Jr., and Bruce K. Waltke, eds., Theological Wordbook of the Old Testament (Chicago: Moody Press, 1999), 241.