The dot product gives the projection of one vector on another. In other words, you get the length of one vector in the direction of the other.

For example, you're taking the trolley. Trolley of mass 1 kg moving forward with acceleration a, and you pull it at an angle of 30 degrees to the ground with a force f = 10 Newtons. So, truck, roughly speaking, is the acceleration of 'a*f=|'a|*|f|*Sin(30) = 5 Newtons.