A tag is a search keyword that you can associate with a game. It can be any word or phrase that's relevant to the game. The most helpful tags describe things like the game's subject matter, style, tone - the kinds of things you might want to search for when looking for a game to play.
Whenever you search for a game, the results will include any games tagged with one or more of the words you're searching for.
Tags are helpful because they let you tell the search engine what concepts and subjects are related to the game. This makes searching easier by letting you find games that are conceptually similar to what you're looking for, rather than searching strictly by the literal title and author.
Tags are also helpful for finding other games related to the ones you like. People are likely to use the same tags for closely related games, so if you start with a game you like, you can look at its tags and search for other games with the same tags.