What is the difference between electromagnetic waves and other waves?
Electromagnetic waves do not need a medium to transport its energy.
There are two types of waves: Mechanical and electromagnetic.
Mechanical waves need a medium, like an atmosphere or water, to transport its energy. Typically you might think of waves like sound. This is because sound is the compression of molecules through vibrations. (This is why "No one can hear you scream in space". Nothing to compress). When you clap, for example, you are distorting the air around your hands. You might have seen sound be expressed in waves, but this is truly the density of molecules.
(You hear sound because of the ear drum's vibrations which is sent to the brain for interpretation.)
Electromagnetic waves do not need a medium as opposed to mechanical waves. In this case a common example would be light. Electromagnetic waves form when the electric field and the magnetic field are perpendicular.
The reason Electromagnetic waves can move through a vacuum is because electric and magnetic fields can exist with out a medium. The reason light interacts with objects, if you are wondering, is the fact that light is both a particle and wave or also known as a photon.