People usually draw waves with wiggles, but it may be misleading. The wiggles represent the envelope of the instantaneous displacement of the medium in which the wave travels. For example, we use the wavy shape of the water surface to represent a water wave, but the wave actually travels in a straight line rather than following the wiggle.
Light is also a wave. More specifically, it is an electromagnetic wave which does not travel in a medium. When an electromagnetic wave travels through space, it causes the electric (E) and magnetic (B) field to change (or oscillate) at corresponding locations. Let's take a look at a classic diagram of how light propagates:
(courtesy of Wikimedia Commons)
The light travels from left to right along the black dashed line (which is straight!). At each location where the light passes though, there are some E and B fields represented by the blue and red arrows. E and B are represented by arrows because they are vectors, which means that they have values and directions at each location. Therefore, everything in this diagram is telling us what's going on at the dashed line. The blue and red curves might be misleading. They are where the arrowheads will be if we plot all of them (but we certainly can't), but they are not the path of the light.
I hope that answers your question. Please follow up if you have further questions.
(published on 09/04/2011)