Divine Stones are the prestige currency of Rise in Time. You get them mostly by winning, so an icon bought with Divine Stones shows off competitive success.
Earning
Winning a ranked Dominion round pays 1 Divine Stone. Events such as Dominion Day can pay them out as well.
Spending
The shop sells 4 icons for Divine Stones, from 1 to 50 Divine Stones each: 4 player icons and 0 team icons.