Why does it have to be 1 specifically? 

It doesn't. It's just a standard. If you want so in your game, you can make all your vectors of length 2. I wouldn't call it normalized though because normalization has a mathematical definition of its own.

As long as you have all your vectors in the game standard (all of them of unit length N, doesn't matter what N is, but 1 is pretty standard), you could still do the direction*speed technique.

All that said, I don't know anyone who uses other unit lengths other than 1. I just want you to know that it doesn't have to be so, it's just much easier for everyone.

How would I use it? 

A normalized vector would signify direction. That makes it convenient to mash up with speed.

For every frame, instead of doing position = newPosition or position = position + movementVector, you could generalize everything with position = position + direction*speed.

#TL;DR

It's just a standard and it makes things easier for everyone.

Simple answer

It's just a standard and it makes things easier for everyone.

More info...

Why does it have to be 1 specifically?

It doesn't. It's just a standard. If you want so in your game, you can make all your vectors of length 2. I wouldn't call it normalized though because normalization has a mathematical definition of its own.

As long as you have all your vectors in the game standard (all of them of unit length N, doesn't matter what N is, but 1 is pretty standard), you could still do the direction*speed technique.

All that said, I don't know anyone who uses other unit lengths other than 1. I just want you to know that it doesn't have to be so, it's just much easier for everyone.

How would I use it?

A normalized vector would signify direction. That makes it convenient to mash up with speed.

For every frame, instead of doing position = newPosition or position = position + movementVector, you could generalize everything with position = position + direction*speed.

Why does it have to be 1 specifically? 

It doesn't. It's just a standard. If you want so in your game, you can make all your vectors of length 2. I wouldn't call it normalized though because normalization has a mathematical definition of its own.

As long as you have all your vectors in the game standard (all of them of unit length N, doesn't matter what N is, but 1 is pretty standard)

All that said, I don't know anyone who uses other unit lengths other than 1. I just want you to know that it doesn't have to be so, it's just much easier for everyone.

How would I use it? 

A normalized vector would signify direction. That makes it convenient to mash up with speed.

For every frame, instead of doing position = newPosition or position = position + movementVector, you could generalize everything with position = position + direciton*speed.

#TL;DR

It's just a standard and it makes things easier for everyone.

Why does it have to be 1 specifically? 

It doesn't. It's just a standard. If you want so in your game, you can make all your vectors of length 2. I wouldn't call it normalized though because normalization has a mathematical definition of its own.

As long as you have all your vectors in the game standard (all of them of unit length N, doesn't matter what N is, but 1 is pretty standard), you could still do the direction*speed technique.

All that said, I don't know anyone who uses other unit lengths other than 1. I just want you to know that it doesn't have to be so, it's just much easier for everyone.

How would I use it? 

A normalized vector would signify direction. That makes it convenient to mash up with speed.

For every frame, instead of doing position = newPosition or position = position + movementVector, you could generalize everything with position = position + direction*speed.

#TL;DR

It's just a standard and it makes things easier for everyone.