Brawl Stars gems are a type of currency that you get by paying real money, and you can exchange them in the game store for customization options for brawlers and more. Virtually, everything that has to do with progressing faster in the game.
However, that is a quick way. There is also a way to get gems more slowly, and that will require us to play the game as often as possible. This way is no other than opening Brawl Boxes, Big Boxes, and Mega boxes. These boxes are obtained through the prize path that offers a season, and in them, we can find power points, new brawlers, coins, and even gems (the rewards varies for each box we open).
There is no way to determine if we will receive gems in each box or not, everything is up to your luck. We may find many, some, or none. On the other hand, getting enough gems to buy a skin for a character or advancing faster in the evolution of the character with the "free" method takes quite some time, so if you want to progress faster, you have no choice but to spend money.
At this point, it is worth mentioning that you should be wary of so-called "tricks" to win gems quickly. In most cases, it will be scammers trying to get hold of your account or payment details; in others, the trick may work, but Supercell could ban your account from their servers. The best you can do is try to get your gems using only legal methods.