Try moving point $P$ horizontally in the z direction. Notice, that the blue vector, the sum of the 'amplitude vectors' from the many electric charges in the sheet, rotates. When $P$ is at a maximum of the wave traveling in the electric field, the real part of the sum, the blue vector, is at its maximum too.

Notice that the wave traveling in the electric field does not decrease in amplitude the farther away it gets, as was the case in previous interactives. That effect can be explained qualitatively as: we view the sheet of charges from a point $P$. Just as with the integration, we imagine concentric rings in the sheet, centered around the nearest point from $P$. The larger a ring's inner radius, the more charges are in it (the width of the rings is constant, but their perimeter increases with their radius). But those charges affect the electric field at $P$ less, because they are further away. These two effects cancel exactly, and we get waves that do not decay, called plane waves.