What is wavelength? I know that wavelength is the distance between corresponding points of two consecutive waves. It is the distance over which a wave repeats its motion. But I am unable to understand what is actually wavelength? What does it really mean?  Is wavelength the length of medium over which one complete wave is formed?
 A: Here's a picture of some waves:

The wavelength is literally the distance between two peaks, or between two troughs, or any other corresponding points on successive waves, as I indicated in the image. If the waves are produced by a constant-frequency source, then the distance will be the same for any choice of location on the wave that you measure. (And for the case of waves propagating away from a point source, as in this image, you'd also want to measure further away from the source, where "near field" [as we call them in electromagnetics] effects have decayed away)
The wavelength is measured in meters (or millimeters or centimeters or kilometers) , because it is an actual distance in space.
A: Consider waves as means to transport energy. Then this follows quickly from the conservation of energy:
Easiest it's explained with a light wave, but a very similar argument can be made for other waves like in the oceans as well:
A a single photon of a light wave has the energy $E=h\nu=h \cdot \frac{c}{\lambda}$ with the frequency $\nu$, wave velocity $c$ and wavelength $\lambda$; $h$ is a constant (the Planck constant).
If we now change the velocity of propagation, (e.g. when moving from the upper atmosphere to the lower or into water; for light the reduction factor is indicated by refractive index), we must keep the energy constant. Then the only thing which can change besides the velocity $c$ is the wavelength $\lambda$ so that the quotient of $\frac{c}{\lambda}$ remains constant.
In water the velocity is a function of water depth, so there a similar relation exists (even when the wave velocity as a function of depth is rather complicated).
Reality is a bit more complicated as you also have effects of dispersion when you don't consider an infinitely long wave.
As to the question "what is wavelength": it is the distance between two maxima or two minima, the distance a whole period of the wave occupies at any given time - there's no other magic behind it. Speaking of a water wave: you take a photo of a water wave, you measure the distance between two wave crests, that's the wavelength. Strictly speaking you need an infinitely long wave; then it is the shortest extent of the spacial periodicity.
