second time around

Between 'second time' and 'second time around',
what's the difference?
I hear 'second time around' often, but don't understand the necessity of 'around'. What makes 'around' significant?

I guess we'd really need to see whole sentences to see what the author had in mind.

Perhaps the 'around' makes the sentence sound/read better, or emphasizes the second occurrence more, instead of the rest of the sentence.

Second time is very generic and simply means the occurrence that immediately follows the first occurrence. Second time around means on the second attempt or encounter, especially when there are only two iterations.