I was shopping for a synth and I realized that I could buy a USB to 1/4 cable and plug a controller into an amp instead. I have no idea what a controller is exactly. Could some one explain? Do they have different voice on them or do I have to use a laptop? And can I do what I was planning on?

a midi controller has no sounds, you use it to control VSTs or sounds in a sequencer or other audio software.
you could use a controller and a laptop to get sounds, then use an amp as a speaker.