Genre

If you think about movies, since there's no interactivity involved, the narrative theme is enough to define an entire genre: thrillers, war movies, romantic movies, comedies, and so on.

Since games are an interactive medium, talking about a war game doesn't really tell us much about it. Therefore, in games, the genre is more informative than the theme and the setting. And so our genres, such as a First Person Shooter (FPS), are heavily related to the gameplay at hand. An FPS can take place in different settings and explore different themes: from historic, to present day or even sci-fi.

Genre tells the players what kind of game they will be playing, and it's a very useful way to classify games. There are quite a lot of genres and each genre might have many sub-genres. Also, smart game designers are constantly redefining genres and pushing the boundaries of what a genre means. Nonetheless, it is safe to say that some genres are universally recognized by both developers and players as standard.

Some examples are FPS, platformers, role-playing games (RPG), sports games, mass multiplayer online games (MMO), Multiplayer online battle arenas (MOBA), strategy games, and simulations. The list goes on and on.

Defining the genre, or having a genre as a starting point for redefining one, is a crucial part of creating a game concept, certainly the one that will most influence the entire design process:

Exercise
How many genres are you familiar with? Make a list of all the genres you know and then highlight the ones you have never played. Get yourself some games in those genres and familiarize yourself with them. Everyone has their favorite genre, but by becoming a game designer, you can't afford to ignore the genres you don't like to play. You are not a mere videogamer anymore!
Have a look at this great list on Wikipedia and keep learning about old games and genres you might have missed! 
https://en.wikipedia.org/wiki/List_of_video_game_genres