somebody is fishing

Somebody is putting out figurative bait, hoping to figuratively catch what he's looking for.

We often hear "fishing for compliments."

Someone may be hoping to discover the truth about some rumor, and pretend to know something (the bait), attempting to trick someone into revealing the truth.

There may be more specific meanings within more specific contexts.

Thanks Avangi for the detailed explanation. When you say "somebody is fishing for compliments", can we make it as "he is trying to win compliments from others"?

RobinG"he is trying to win compliments from others"?

Right. Except that quite often, instead of doing good deeds to win them, he may engage in self-deprecation, expecting others to reassure him with kind words.
You might say he is simply putting out the bait.

Got it ! Thanks Avangi.

RobinG What does the sentence"somebody is fishing" mean from a non-literal perspective?

It may be worth noting that the practice of putting out bait to trick people on the net into revealing their personal information has become so common, it has its own spelling: "phishing." It's the same basic idea.

Thanks Avangi, good to know that.