A vector has both magnitude (which is its length) and direction (which is its angle).
Any two dimentional vector at an angle will have a horizontal and a vertical component .
A vector written as ( 12 , 8 ) will have 12 as its horizontal component, and 8 as its vertical component, and because both components are positive, the vector is pointing to the northeastern direction.
Often when two processes interact we only know the component vector values and need to be able to combine these to get a desired result.
This might be more easily understood by an example:
Suppose I am trying to fly from point A to point B which is due North of point A. My plane flies at an air speed of 100 miles/hour but there is a wind blowing due West at 30 miles/hour. How many degrees East of North do I need to orient my plane to fly in a straight line to B?
From the above diagram, I need to head my plane (approximately) #17.5^o# East of North.
This problem could be extended to ask:
If it is 200 miles from A to B and my plane has enough gas to fly 250 miles will I be able to make this trip?