A transverse wave is a wave that oscillates across the 2-dimensional plane that it is travelling in. It may oscillate either vertically or horizontally, and this refers to its polarity. Electromagnetic waves come under this category. Imagine a slinky on a table, if you move it to the left and right, or up and down it would represent this type of wave.

This is opposed to longitudinal wave which include sound, ripples in water, and certain types of earthquakes. This exists as compressions moving through the plane in which it is travelling. Energy from this wave is transmitted as mechanical energy. An example would be a slinky which was pushed forward and backwards, compressing and extending it as the motion of the wave was transmitted.

Light is composed of transverse waves. See Electromagnetic spectrum for information on different types of electromagnetic waves.