You can triplicate your offline earnings using gems when you open the game. 
 
You could also use gems to skip construction times when you want to build a new area in your precinct. Just select the area that you would like to build and start the construction work. Then, the game will allow you to pay with gems to instantly have your new building.  
 
Moreover, gems can be used to buy card packs (tap on the card's icon, right side icon on your playing screen) and obtain epic cards. They will bring permanent upgrades to your police stations and special characters. Read carefully their descriptions!