The Kree and the Skrull are two galactic empires, the former tending to very good with artifical genetic evolution, nanotech, and power generation, whereas the latter are shape-shifters who are incredibly good at infiltration, espionage, and copying the powers of their enemies. One way to think of them is that the Kree are very much about hard power, whereas the Skrull are very much about soft power. 

The idea of the Kree-Skrull War is that these vast galactic powers, locked in war, threaten to come to blows with Earth as the battlefield, “the cosmic equivalent of some Pacific island during World War II.“ The Kree see Earth as an important outpost because of their connection to the Inhumans, and indeed Ronan attempts to devolve earth back to prehistoric days so that it can be better used as a military base. The Skrulls, meanwhile, want to capture the original Captain Mar-Vell and disrupt the human superhero teams they believe to be Kree allies (the Fantastic Four and the Avengers, primarily). 

Eventually, the good guys save the day and stop the Kree-Skrull War, resulting in them agreeing to leave Earth out of their conflicts.