When used as an auxiliary verb (together with the infinitive of another verb), mieć means “must / have to / need to”. Sometimes it can also mean “supposed to”, as it does in this particular sentence.
- Masz to sprzątnąć! (You have to clean this up! [imperative, not very polite])
- Powiedział, że mam oddać mu pieniądze. (He said I need to give him back the money.)
- Mamy się spotkać o 19:00. (We’re supposed to meet at 7PM.)
The “must / need / have” meaning might feel a bit distant from “supposed to”, but if you think about it, in English you can often express pretty much the same thing with the two (He said I need to give him back the money. = He said I am supposed to give him back the money.)
You should note, however, that “mieć” is mostly used to express obligations that have something to do with other people – in other words, social arrangements, requests, commands, etc.
If you’re doing something of your own volition, “mieć” won’t be the right verb to use:
Muszę się nauczyć polskiego. (either because that’s the goal you set for myself, or because someone else expects that of you = internal / external obligation)
Mam się nauczyć polskiego. (you can only say this if someone is making you learn Polish, and not merely hoping that this will happen = strong external obligation)
All in all, the Polish auxiliary mieć doesn’t have anything in common with the auxiliary have in English, which is used to express the perfect aspect.