A combo is a single unit containing both the pre-amp (distortion, gain, EQ, etc.) controls and speakers.
Not all preamps contain tubes, however. Solid-state (SS) amps do essentially the same things digitally (someone can probably help me out here--I'm not sure "digitally" is correct, but I don't know the proper terminology). Companies have worked long and hard to get SS to sound like tubes (like TVs used to have), but it ain't the same (I'm sure someone will take exception to that). The advantage to SS is that you never have to replace the tubes, which can be costly depending on how many you have.
The advantage to having separate head (head contains preamp) and cabinet is power and versatility.
=my two cents