EGNOS is the European equivalent of WAAS. It works with ground stations with GPS equipment that are constantly making observations of the signal emitted by the satellites overhead. This information is sent back to one particular satellite and some GPS units can use it to compare with what they register themselves. This way it is possible to make up for errors that are caused by slowly changing conditions such as ionospheric interference.
It's important to notice that a GPS device with only WAAS is not going to be more accurate than one without it. Only EGNOS enabled devices will improve accuracy.