Prepositions connect words and groups of words together. They express the relation between living beings, things or contexts. German has many different prepositions. You've already learned about location prepositions that give information about a place, position or direction, and temporal prepositions that refer to time. Knowing how to categorize and when to use them isn't always easy because they can mean different things depending on how they're used. In many instances you can only know the meaning of a preposition from its context.

Some prepositions serve the function of connecting a verb to an object. In other words, they don't describe a relationship (location or temporal). Such prepositions are simply fixed to certain verbs. For example,

demonstrieren gegen + accusative:
Wir demonstrieren gegen das Experiment.

sich engagieren für + accusative:
Wir engagieren uns für die Natur.

warten auf + accusative:
Ich warte auf dich.

Since there is no strict rule that says which prepositions must be used with which verbs, it's better to memorize such verbs along with their prepositions and case.