This idiom or expression means:

Under the influence of what’s happening at the moment.

When someone says “I’m in the moment,” they mean something like “I’m focusing on what’s going on right now; no past regrets, or future worries.”

When someone says “I was caught up in the moment,” or “I was acting in the heat of the moment,” they mean something like “I did what I don’t usually do. I didn’t know what I was doing. I was affected by what was happening at the time. Etc.”