Tubes refer to actual vacuum tube technology that a lot of popular and upmarket amplifiers use to get their astounding volume and legendary tone. They emit electrons from the lightbulb like filament inside or a cathode. The technical details of how a tube works is pretty complicated and not something I am 100% familiar with the intimate mechanics of but what I can tell you it there is practically nothing like playing through a good tube amp. There are many different kinds of tube amps and tube types which call give different sound characteristics such as EL34, 6L6, EL34, KT-88 and so on. Tube amps can very easily be modified sometimes as simply as changing your tubes. Solid state amps are amplifiers that don't use any tubes (besides hybrids) and emulate tube technology by using transistors instead. There are still a number of good sounding solid state amplifiers out there for many sonic purposes. Most solid state amps use analogue technology. They are often a lot lighter and simpler than their tube counterparts.
A head is an amplifier unit minus the speakers. A cabinet is an enclosure with the speakers only. Some popular speaker configurations for guitar amplifiers are 1 12" speaker, 2 12" speakers or 4 12" speakers though sometimes you can get even more or even bigger speakers like 2 15" speakers. Popular cabinet configurations for bass speakers are 2 10" speakers, 4 10" speakers or 1 to 2 15" speakers. They are often called a "cab" for short. A head is the "not combo" which is the amplifier unit in it's own chassis without any speakers. This is designed in a way that you can hook it up to just about any cabinet of your own choice and mix and match sounds. A combo is exactly what it sounds like which is a combination of the amplifier unit and speakers all in the one chassis (cabinet actually refers to the chassis that holds everything together in either a head, speaker cab or combo).
Many popular amps are in the combo format like Fender Twin Reverbs, Blues Juniors etc. and early Mesa Boogie amps like the mark I through IV. Many modern amps are most commonly used in a head format like Marshall, Mesa Boogie Dual Rectifier, Soldano SLO, Peavey 5150 but are also available in combo form. It is very easy to find all kinds of info on these things on the internet and even with the forum's own search function. We are always happy to help out. Let me know if you require any further clarification.