Gems are very important in Clash Royale. Having Gems allows you to open up different chests you obtain from Arena. There are a few ways to receive Gems, all of which give you varying amounts of Gems as rewards. Not all chests will yield Gems, but Free Chests and Crown Chests will do so on average of 2-4 Gems as rewards.
You can also purchase Gems from the in-game Shop for real money. Gems can be purchased in bulk for varying prices. Here is a list of the options available for purchasing Gems from the Shop with real money
Having Gems on hand for opening chests can get very tricky, especially if you are playing the game for free and don’t want to pour a lot of money into the Shop. But there is some ey things to keep in mind and get the most out of your hard earned Gems