"Can you carry my bag for me?"
Translation:Kan du bära min väska åt mig?
Yes, as many prepositions it has several possible meanings. One is toward(s) as you mentioned. I’d say these are the main ones, then there are smaller nuanced usages. And then it is used as a verb particle in a lot of verbs which is better just learnt with the verb, like göra något åt något (do something about something).