The main role for this move is the one you already know, to lock the foe with an move who is not very good to be using all time. Both in single, double, triple, and rotation formats.
But sometimes, if you find the right situation, you can improvise. For example, if your Pokemon has the ability Sap Sipper and you make it use Encore on a Pokemon who just used a Grass type move, it will give a large amount of support, especially if it's the last Pokemon of that player. And everybody knows by experience that some players usually use the wrong moves a bunch of times, and are not able to predict most abilities. So you can take advantage of their inexperience.