Predictable time-based occurrences are described using this phrase to emphasize the cyclical nature of time.
"The boxer started to come around after being knocked out in the third round". COME AROUND
"Investors have started to come around to the view that the U.S. economy is more insulated from oil prices". COME AROUND
"Come around" is closely linked to several other idioms and phrases that share similar themes of return or consequence: COME AROUND
In healthcare contexts, "coming around" is a standard colloquialism for the moment a patient wakes up.