There are three particularly useful unit vectors often
called either 
and 
or 
and 
depending on what
book you read. When you plonk down your coordinate
system, the vector 
points along the direction
of the x axis, and 
points along the direction
of the y axis. Similarly for and the z axis.
And you already know because of the little hats that
these are unit vectors. That's all to these cute little
vectors. Why are they useful? Well it's mostly a notational
thing. Suppose I want to write the vector 
in
terms of its components. Then using and
you can write (in two dimensions)
Why is this right? Well because 
is a vector
kind of like 
and 
like 
,
so when you add them together you get the original vector
. Of course in three dimensions the equivalent
formula is 
.
So this is a very convenient way of representing a vector in terms of its components.