Gems are the virtual currency replacing Lingots which is available for all iOS users. Many Android users will also see their Lingots replaced with Gems, and Web users will still see Lingots. You will continue to earn Gems as you would have earned Lingots for completing lessons on Duolingo. Typically you will earn your gems when you meet your daily goal.
You can use your Gems for purchases in the app/web shop. To access the store, tap the Shop tab. If you're a web user, you can click here. You will see your total number of gems/lingots displayed in the shop. You can use your Gems for a variety of app features, such as a streak freeze, heart refill, streak wagers, outfits for Duo, and Bonus Skills*
*Bonus skills (Flirting and Idioms) are not available for all courses.