Use when a meeting or conversation results in strong feelings of hope, relief, disappointment, etc. We came away relieved that the issue was finally resolved.
Pro Tip 2/3
Physical Departure
Use 'come away' to emphasize the action of leaving a place, especially after an event. Guests began to come away after the celebration ended.
Pro Tip 3/3
Mutual Separation
Implies leaving together with someone else, not alone. My friend and I came away from the party early.