Cartesian vectors are vectors that are represented in cartesian coordinates.
They can be written in the form (a, b), where the vector is 'a' units right and 'b' units up from the tail of the vector to its head.
They can also be represented on a cartesian system of graphs.
An example of a cartesian vector in two dimensions is (1,2).
The vector is drawn below with its tail at the origin:
