I've been trying to get the hang of vectors and I read Wolfire's blog about linear algebra and I seem to understand most stuff except when it comes to storing a direction as a vector and using it by multiplying the velocity by it. I know it has to be normalized (have a length of 1), but why does it have to be 1 specifically and how would I use it? 

Also how would I represent it in 2D [x,y] coordinates. For example if I wanted a direction such as North-East?