"Feeling sorry for" someone means that you feel bad because they feel bad, or because they're in a difficult situation.

For example, you can "feel sorry for" a person who:

• was just broken up with by a boyfriend or girlfriend
• got fired
• has never had a chance to eat your favorite dish

and so on.

Grammatically, you can use this phrase in these ways:

I feel sorry for them.

I feel sorry for them having to work so late.