Let's say that you want to get to A from O. That is, you want to go from where the vector starts (O) to where the vector ends (A). You want to do this by first going along the positive x-axis and then going along the positive y-axis. So, you go from O to B and then B to A.
The x-component of a vector is how much you go along the positive x-axis, before you reach the vector.