In the U.S., television shows run in "seasons". A show usually has one season per year. The season has somewhere between 8 and 24 episodes.
The "season premiere" of a show is the first episode in that season. So, for example, if a show that you like finished six months ago, and yesterday a new episode came on last night, you can say:
I saw the season premire last night.
Shows also have a "series premiere", which is the very first episode of the show.
The opposite of a "premiere" is a "finale":
The season finale is next week.