Due to StarCraft spanning quite some time both in our time and in the fiction itself, the story can be hard to get a handle on at some points. Thankfully Blizzard has published a short animated video that helps explain just what the Protoss are up to in Legacy of the Void.
The basics of the story is that the Protoss at one point were a warring race within their own culture, but then united and became quite peaceful and powerful. Then the dark templars were cast out for believing differently from the powers that be and caused another civil war within the Protoss. This led to the Zerg invasion of their home planet, and now Artanis is about to launch an invasion to take it back.