The most famous aspect of the Songkran celebrations is the throwing of water. The custom originates from spring cleaning aspect of Songkran. Part of the ritual was the cleaning of images of Buddha. Using the 'blessed' water that cleaned the images to soak other people is seen as a way of paying respect and bring good fortune.
It also doesn't hurt that April is the hottest part of the year in Thailand, so being soaked is a refreshing escape from the heat and humidity.