In many pieces of literature, light is said to travel like a "wave". Does this mean the light literally propagates through space like a wave as in up and down and so on or does light move linearly through space? Also, if it move linearly, why do we say photons are a wave then?
This answer is in addition to the answer by Sofia, on the classical electromagnetic wave, i.e. light, and replies to the title.
Do Photons Move in a Wave Like Pattern
Photons build up the electromagnetic wave. They are elementary particles, and as such are governed by quantum mechanical equations and rules. The rules applied, there is consistency between the individual photon behavior and the behavior of the collective ensemble, light. Light is an electromagnetic wave.
These images from wikipedia might help:
The electromagnetic waves that compose electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized EMR wave propagating from left to right. The electric field is in a vertical plane and the magnetic field in a horizontal plane. The electric and magnetic fields in EMR waves are always in phase and at 90 degrees to each other.
This oscillating behavior of the fields is similar to transverse waves on a string, though there does not exist a medium that is oscillating, but just the fields.
Left and right handed circular polarization, and their associate angular momenta.
It is not simple.
The are two approaches about how light moves, and they are both correct. One is geometrical optics that describes the way light passes through lenses or is reflected by mirrors, etc. It refers to the light as moving according to straight lines.
But there is another way to treat the light, I'd say a deeper approach. Light is indeed waves. Did you hear about Huygens' principle? It is the heart of the wave-like behavior. To understand what I talk about I suggest you to look at the figure in Wikipedia, the 3rd figure. It shows a very small slit through which passes a wave - it can be very well a wave of light. What you see in that figure is indeed the illustration of the Huygens principle.
The Huygens principle says that from every point on a surface of constant phase, develops a small spherical wave that increases and increases all the time. At any time the envelope of all these spherical waves is a new surface of constant phase, and on it, again develop from any point small spherical waves whose envelope is a new surface of constant phase, and so on. So the wave of light advances in space.
Probably you will ask what is a surface of constant phase. Well, for the moment consider that you have a source of light that emits a parallel beam of light. A surface of constant wave will be a transversal section through this beam, as you see in the moving figures 2 and 3 at the site that I recommended you, on the left of the screen. But, on the right of the screen, after the slit, do you see how from each point on the slit develops a spherical wave? Figure 3 illustrates approximately one such point, because the slit is small. But figure 2 shows many such points because the slit is wide. From each such point develops a spherical wave, and at some distance from the slit you can see the envelope its form is something between a line and a circle. Do you see how it propagates? You have to keep in mind that these envelopes are also surfaces of constant phase and from each point on them develops a spherical wave, and the next envelope is just the envelope of these spherical waves.
Not so simple? Then leave me questions and I'll answer you tomorrow.