A box is put on a frictionless ramp. 
(Often referred to as an inclined plane)
It begins to slide.  The bigger q is, the more the box's acceleration will approach "g" or 9.8m/s/s.
Of course, gravity provides a vector pointing straight down.
The surface also pushes back on the box (remember the 3rd law?).  The angle q is between "mg" and "mgcosq". We know these two vectors must be the same length because the box is not moving into the plane; it only slides along it. The orange vector is called the "normal".
The box feels a net force down the plane, and acelerates that way.
Where did the sin & cos stuff come from?  Well, look at the shapes involved here; they are 90° triangles, which we have already studied.

So, the net force acting on the object is given by:
F = mgsinq
The acceleration is given by a = F/m, or in this case
a = mgsinq/m = gsinq