“I think he's still hung up on her.”

You're gossiping about a friend of yours who recently separated from his wife. You say this because you think that he still wants to get back together with her.

I think he's still hung up on her.

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(someone) is hung up on (something)

Being "hung up on" something means to be really worried or upset about something, so that you can't stop thinking about it. You can "be hung up on" a person, which usually means that you have romantic feelings for that person that aren't being returned. Or you can get "hung up on" an idea:

Don't get hung up on the details. Just try to do your best.

People get so hung up on brands and labels.

There's a totally different meaning of "hung up on" as well. When you "hang up on" a person, it means that you end the phone conversation with them suddenly:

He hung up on me! What an asshole!

Notice that that's different from:

He's hung up on me.

...which means that he's obsessed with you or in love with you.