This is a bit oversimplified, but--reverb in amps is a simulation of the natural reverberation you'd get in an enclosed space that reflects sound, such as a church, gymnasium or even a bathroom with a lot of hard tile and reflective surfaces. In amps it can be created either by a tank that has springs in it, or in some more modern versions that do this digitally. Listen to Dick Dale for some recorded examples of this, or "Pipeline" by the Chantays which is a classic example.
Tremolo (sometimes mistakenly called "vibrato," as in the case of old Fender amps), is a regular variation in the volume level of the signal coming out of the amp. There are different ways of doing this electronically, which can yield different "flavors," and on many amps you can vary both the speed and intensity of the effect. Probably the most extreme example of this I can think of is the guitar on "Crimson and Clover" by Tommy James and the Shondells (and about midway though the song, they run the vocals through some kind of tremolo effect, although I don't know exactly what it is).