Get a barrel or steel drum, drill some small holes at the bottom of the barrel. Dig a hole and place a bed of stones at the bottom. Place barrel inside hole on top of bed of stones, cut a hole to fit the end of the PVC pipe so that the pipe is inside the barrel near the top. Fill the barrel with 1/2" to 1" stones. Cover barrel with a top and regrade side of hole with top soil. Basically, we are creating a collection area for the water instead of it running free out of the pipe. The size of the barrel (collection area) depends on how much water needs to be drained off.
As @Michael has said, you could also extend the pipe and create a drainage bed as the water is moving down the pipe. (Similar to barrel concept)
Another idea is to create some obstructions at the end of the pipe to re-direct the water or slow it down, then there would be less erosion. Even a bed of stones or large rocks at the end of the pipe would help with the erosion as the water would hit the stones/rocks first and disperse before hitting the soil. Those are less work. A nice arrangement of rocks and pebbles could do the trick.
If you want to hide it, then a more elaborate drainage system would be needed.
