An electromagnetic wave is a wave in which an electric field and a magnetic field keep creating each other as they travel. The figure draws the electric field in the vertical direction and the magnetic field into the depth. The two stay at right angles to each other, both are at right angles to the direction of travel, and they swing in phase. Nothing is being squeezed the way air is squeezed by sound. The swing is across the direction of travel, and it can cross empty space because what swings is not matter but the fields themselves.
The last two Maxwell equations are what make this wave. The Faraday law says that a magnetic field changing in time creates a curling electric field. The Ampere and Maxwell law says that an electric field changing in time creates a magnetic field. A change in one makes the other, and the change in that one makes the first again. The chain never breaks, so a wave that has once left its source keeps going without it.
The speed does not come from any material. It follows from the permittivity and the permeability of empty space alone. The value those two give is about 299.8 million metres per second, which matched the measured speed of light exactly. That match is how we learned that light itself is an electromagnetic wave. The equation panel carries the formula.
Moving the frequency changes the wavelength. The speed stays the same, so more swings per second means a shorter length for each one. The panel runs from 405 to 790 terahertz, which is the range the eye can see, roughly 380 to 740 nanometres. The colour of the electric field in the figure follows that wavelength, long towards the red end and short towards the violet end.
The two fields are not the same size. The magnetic value is the electric value divided by the speed of light, so on a single scale the magnetic curve would be almost flat. The figure therefore multiplies the magnetic field by the speed of light to bring it up beside the electric one. The shape and the phase are untouched, so you can still see the two peak together and trough together.
Turning on the energy flow adds arrows along the direction of travel. This is the Poynting vector, fixed by the cross product of the two fields, and it says which way and how much energy the wave carries. Its size goes with the square of the swing, so it is longest at the peaks and troughs and almost vanishes at the nodes. Sunlight warming the ground and a radio wave shaking an antenna are both this energy being received.
The viewpoint can be tilted. A shallow tilt flattens the depth and hides the magnetic field, while a deep one lets the two fields overlap and become hard to tell apart. Dragging sideways on the canvas turns the view the same way, so look at the two fields from several angles to see how they stand.