I believe wikipedia explains it better than I could:
Dot product - Wikipedia, the free encyclopedia
Or did you have more specific questions?
The explanation that is the most easy to visualize:
the dot product is a scalar projection of vector A onto vector B.
If you think of it this way, then for example the following properties of the dot product become intuitively clear:
-if vectors A and B are parallel, then the dot product is equal to the length of vector A.
-if vectors A and B are perpendicular, then the dot product is zero-
-the dot product can never be larger than the length of vector A