In horror movies, you'll see a lot of blood splattering on walls. Ick. To splatter is to splash liquid. A splatter is also the spot the liquid makes.
When you spill some liquid on the ground, the sound it makes is splat. Splash a lot of it, and you have a splatter — drops of the liquid across a large area. If you are frying meat in a hot pan, the grease will splatter across the stove and counter near it. In the figurative use, gossip about a celebrity's mishaps is often splattered throughout a gossip magazine like spilled milk on a floor.