John Frame's Systematic Theology, chapter 11
God acts in miracles, providence and creation, all with a purpose. That purpose can be described as His decrees - what He ordains to bring to happen. Though the word "decree" doesn't appear in Scripture often, these words do: plan, counsel, purpose, will, pleasure, etc.
God's decrees covering all things shows His Lordship over everything, that He intends everything for a reason. His interpretation of the facts precedes the facts (Van Til). In other words, everything is as it is by His design and decree.
God elects a people historical sense and in an eternal sense.
Historically, Israel was and the church is God's people. This choice was by God's grace, not their merit (Deut 7:7-8). But people can forsake God and be removed from this historically elect group by their unfaithfulness (Saul, Judas, excommunication, etc.). We don't have to say they were never elect in the historical sense, as we do in the eternal sense (1 John 2:19). Not all of this group are eternally elect. This category is alive and well in the NT, too (Acts 5; Heb 6:4-6; Rev 2-3). Jesus is the ultimate elect of Israel, the faithful remnant and branch (Jeremiah 23).
Eternally God forgives the sins and writes His law on the hearts of His eternally elect (Jer 31:31-34; Rom 8:29-39). This does not depend on our ongoing faithfulness, for God keeps these faithful.
These two senses are meant to go together. We see historical election, and so have a "limited knowledge" of eternal election.
Eternal election implies reprobation. God choose not to save some. Romans 9 shows this, especially verse 22. This doesn't mean we aren't responsible and guilty when we reject God ourselves. It doesn't mean we need not offer the Gospel to all men. It doesn't take away from our assurance, which should come from looking to Christ's promises, not eternal decrees.
The order of God's decrees has prompted lots of debate. Did God elect His people from their fallen state, or before they were created? Supralapsarian says "before the Fall." Infra-lapsarian says "after the Fall." Frame says we shouldn't take sides, as Scripture doesn't let us into God's priorities and thought processes this minutely. The infras are right that God chose us out of sin, so the Fall is in view. The supras are right that God has a plan for His people beyond the Fall and created history. In my view Ephesians 1:4 answers this question very decisively on the supra side, but the infra concern about the sin context should not be dismissed.