Individual applications don't but open your task manager and look at how many processes are running. The more cores you have the more processing power the operating system has to distribute all those processes, and their threads, across. Furthermore some graphics programs and game engines sometimes use upwards of a dozen worker threads.
CPU power in general hasn't lept by great bounds in the last decade like it did 20 years ago when every new computer would be outdated in a year, so now the best strategy is to add more cores so each individual core isn't as burdened as it would otherwise be, and it will likely be the only strategy when we reach the limits of silicone based CPUs in the near future due to quantum tunneling unless someone comes up with something better. Stacking transistors could also be a possible solution sort of like a CPU skyscraper.