You can picture a vector as an arrow, pointing in some direction and having some length.

The vector (1, 1) has a length of 1.414 (by the Pythagorean theorem). Normalizing this vector sets its length to 1, so the vector becomes (0.7071, 0.7071).

Normalized vectors, since they have a length of 1 are very useful for representing directions, and you can then multiply them by any number to scale them to any length you need, such as the velocity length in the example you posted.