An electromagnetic wave is a disturbance in the electric and magnetic fields in space. Figure 12.16 shows how we can represent such a wave. In this diagram, the wave is travelling from left to right.
The electric field is shown oscillating in the vertical plane. The magnetic field is shown oscillating in the horizontal plane. These are arbitrary choices; the point is that the two fields vary at right angles to each other, and also at right angles to the direction in which the wave is travelling. This shows that electromagnetic waves are transverse waves.