English speakers use the sound "um" when they don't know what to say next. Here's an example from a TV talk show:
Well, my daughter in this show is very strongly liberal, and she's a very — she's a — she went to, uh, um, Stanford Law School, and she graduated from Stanford with honors.
But people also use "um" when they're talking about a topic that is uncomfortable. Using "um" shows the listener that you're being careful about a topic that is very sensitive. So you might use "um" when you're talking seriously about:
- a death in someone's family
- a decision at work that you disagree with
Listen, um, I know that you're having a hard time financially right now, but I really need your rent check.
By the way, you might hear or read somewhere that you shouldn't use "um". That's a rule that English speakers are taught in school, because some people think that using "um" too much makes you sound unprofessional. But almost everyone uses it from time to time. As an English learner, it actually makes your English sound more natural when you use hesitation sounds like "um".