"Initial Touch" means that the harder (or faster) you strike the keys, the louder the voice sounds. The timbre (character or quality) of the sound can also change, depending on the keyboard or voice you are using. For example, if you choose a brass voice and strike the keys hard, you might hear a "fall".

"After Touch" is like Rosetree said; once you strike the keys and are holding them down, if you push down harder, it will produce either a vibrato, a swelling in sound (where the volume gets gradually louder) or some other effect.

Hope this helps.