The system output y(t) is the system input x(t) convolved with the impulse response h(t).
Flip h(t) and slide it past x(t). At a given location, the area of the product yields y(t) for that location.
h(t) is flipped because points further back in the input signal x(t) will generate contributions to y(t) from further forward in their impulse responses.
The demo can be run off-line using a hard-copy downloadable as a .pdf file here.
Print on an 8.5" x 11" overhead transparency, cut in half on the dotted line, flip the top half and slide it past the bottom half.