Gems are just a premium currency designed to make you pay for duo.
Challenges, power-ups, streak-freezes etc.. all cost gems. The goal is that you spend on boosts and stuff, and then when you miss your streak and you're out of gems, you can either drop you streak or pay for gems. You'd be surprised how many people pay for gems.
I've been on duo almost a year, never missed a streak and have not needed to bother with gems at all.