Shrines are the crystalline structures scattered around the map. On the traditional 3-lane map there are four shrines in a line down the center of the map. The single lane map only has two shrines located towards each sides starting base.
It is very beneficial to captured the shrines, they give your team a minor buff which stacks based on the number of shrines you control. The trophy is cumulative across matches so it should only take you a few games to get this.