Mater, non-colloquially, means “to tame” or “to overcome a difficulty”.
J’en ai maté des plus coriaces que toi.
I’ve tamed tougher guys than you.
Colloquially, it means “to watch”, “to look at”, “to ogle”. It is mostly used with movies and people, especially girls. When talking about girls, mater is usually pejorative.
T’as maté le dernier épisode du Trône de Fer ? (The official French translation of the title is “The Iron Throne”.)
Did you watch the last episode of Game of Thrones?
Arrête de mater ma sœur, gros dégueulasse !
Stop looking at my sister, you pervert!
There is also a verlan version of this word, téma, mostly used in the imperative.
Téma la meuf !
Look at that chick!
Listen to the examples: