When objects are represented on a computer screen they are stored in memory as a whole lot of points which are joined up and manipulated (mathematically) such that they make pretty pictures. Each point in this imaginary space is called a point, and a line joining two points is called a vector. As you can imagine, to represent a point in two dimensional space you will need two values which represent its location (or coordinate) on a cartesian plane. Vectors are normally dealt with as originating at the origin and ending at a given point.
This is an example of a point.
And a vector from the origin to that point.
The length of the vector from its origin to end point is called the magnitude. This is the formula to calculate a vectors magnitude.
For comprehensive explanation on vectors check out the wikipedia entry.