Notes on John Frame's Systematic Theology, chapter 7
God acts in His world so we will know He is the Lord (Exodus 7:17 for just one example of many). Knowing who God is (attributes) depends on knowing what He has done (acts). We look first at what God has done.
A miracle is "an extraordinary [highly unusual, impossible] manifestation of God's covenant lordship." Many define it as an exception to natural processes, but this isn't always true (Ex 14:21). They aren't always immediate, either (lacking a secondary instrument besides God's direct power). Miracles almost always prove a prophet is really from God, but there are other purposes of miracles in Scripture (Flood for judgment, incarnation for salvation, healing out of compassion, etc.). Miracles don't just prove revelation; they actually reveal God's control, authority and presence to us.
Miracles occur today, but "only at God's own initiative." They aren't a normal experience for a believer, but rare even in the Bible. Believers shouldn't feel guilty for not experiencing them.
Miracles don't so much prove God exists, as they assume God to make sense. We cannot demand them before we believe in God. David Hume ruled miracles impossible by definition, and many modern liberal theologians follow suit. Miracles are evidence, though, that call and obligate us to believe in Jesus as the Christ. Miracles are a kind of revelation. Those found in Scripture are historically true and accurate, because Scripture is.