Waves come in two kinds. In a transverse wave the swing is at right angles to the travel; in a longitudinal wave the swing is along the travel. The top of the figure is transverse, and the marked point only moves up and down. The wave goes right, but the point itself is never carried right.
The bottom of the figure is longitudinal. Each point rocks back and forth along the direction of travel, so places where the points crowd together alternate with places where they spread apart. Sound is this kind, and it is those compressions and rarefactions that reach the ear.
An electromagnetic wave is transverse. What swings is the direction of the electric and magnetic fields, and that direction stays at right angles to the travel. That one fact already separates it from sound.
Take a single slice across an electromagnetic wave and you find one electric field and one magnetic field standing there. The two are at right angles to each other, and both are at right angles to the travel, written , where points along the travel.
Those right angles are not a coincidence. Empty space holds no charge, so the Gauss law leaves the electric field with no component along the travel. The same argument runs for the magnetic field through . Only the components across the travel survive.
The figure tilts the magnetic field into the depth to fit it on a flat page. In reality the plane of the electric field and the plane of the magnetic field cut each other at a right angle, and the line where they meet is the direction of travel.
The electric and magnetic fields peak at the same place at the same moment, and trough together too. That is what being in phase means. One of them is never at a peak while the other sits at zero.
The figure draws the two on separate lines. Laid on top of each other the curves would cross and the timing would be unreadable, so vertical lines connect the peaks instead. Those lines always cut both curves at a peak, and that is the whole content of the word.
Their sizes are not equal. The relation makes the magnetic value the electric value divided by the speed of light. On one scale the magnetic curve would be almost flat, so the figure multiplies it by the speed of light to bring it into view.
Sound travels only through air or water or metal. What swings is the material itself, so where the material ends the sound stops. That is the top row of the figure.
An electromagnetic wave crosses empty space. What swings is not matter but the field itself. Sunlight reaches the ground across 150 million kilometres of vacuum because of this.
In the nineteenth century people assumed there had to be a medium carrying light and called it the ether. Experiment after experiment looked for it and found nothing, and that failure was one of the clues that no medium is needed at all.