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In the most mondane sense, this is an electrical device that "rectifies" electricity. Here is a very simple explanation.
You have a 110 Volt AC power socket in your house, that is the power socket that gets "fed" by the PG@E grid wich "pumps" AC power through the wires at a frequency of 60 times per second. That is where the notion of 60 Hertz comes from. As an aside, there are countries that have different voltage, some have 220 Volts ( in general all of Europe has 220Volt, except of course England as they decided to go with 240 volts) and they all run a 50 Hertz frequency. So, in Europe you can easily pull 3000 Watts out of a power socket and a hair dryer for instance can be twice as powerful as here in the US where you can just about pull 1750 Watts out of a line before the tripper gets tripped.
Now what is the frequency. AC voltage is ALTERNATING Current, it goes from zero to plus, back to zero, then to minus, then back to zero ( it is a alternating wave) . DC on the other hand ( DIRECT Current as in a 1.5 volt battery) does not switch polarity it stays on 1.5 VOLT until the batterygets empty.
So, how do you get from AC to DC.... yep... you "RECTIFY" the power, that, for instance is what your power supply connected between your laptop and the AC outlet on the wall does. You can also get a device to go from DC to AC and that is called a DC to AC converter. Simple he?
Here is some stuff on the rectifier story.
The rectifier started really in the 1940, first with selenium rectifiers, than silicon rectifiers and these devices typically were used in industry to convert power to power equipment and machinery. Then the consumer market came and these rectifier devices needed to be made small, cheap, better etc etc and there is a whole slew of different technologies that do that, one of them is a tube rectifier and another one is a solid state rectifier (transistor). If you need more details go wiki on this. So what is the problem with a solid state rectifier when used in a sound applifier ( HI-FI , Music / band amplification) and why does that sound so "bad" compared with the tube rectifier or... perhaps a better way to state is ... why does the transistor rectifer sound so "harsh and "painfull" compared with the bottle ( tube rectifier) especially with the first generations of silicon rectifiers?. That, folks has to do with harmonics and how the human ear hears sounds. Odd and even harmonics are the issue here. For instance, 2nd harmonics sound "different" when compared with 3th harmonics. So, the ones generated by the Tube rectifiers make substantially more of the "pleasant" ones.
Here is your homework: Find which harmonics are pleasing/ pleasant to the ear and which ones are not. Hint : it is either even or odd hormanics ( ea 2,4,6,8 or 3.5.7.9).
So, why are the later Silicon rectifier much better than the first generation devices. Well, there are some newer technologies. Check out FET (Field Effect) Transistors and you will see that those transistors are generating harmonics "closer" to the spread generated by the tubes. Hence the fact that recent MOS of FET transistor amps sound pretty close to the old bottle ones.
One more thing, lots of the "grit" of the sound really comes from the ability of the transformer to power the tubes / transisters to very high voltages and that mean expensive transformers and heavy buggers too. So, cheap amps will save a buck in that area and therefor will not get as close to the bottle sound as other better designed and more expensive amplifiers ( Marshall, Vox, Peavey and others). Good??
Now here is some more useless information.
Your electric clock keep time pretty good he? Wel it uses the AC "pulses" to "count (the 60 HERTZ pulses) and moves the dial accordingly. Clever he??
So the power generating system keeps perfect count of the amount of pulses it has to do in a given time but they DO sometimes run slower ( like 1 or 2 pulses) in a given time period. The good folks at PG@E then increase the speed a bit until they have caught up. Now you know.....

So, by now the headache is gone so let's talk a little more about the difference between tube amp and "transistor" amps. There are situations / uses where a transistor amp sounds better than a tube amp. For instance, a pedal steel guitar just sounds MUCH better through a Transistor amp and in some cases , you will find that amplifying an acoustic guitar also sounds better with an amp specifically "voiced" to cater for that instrument ie a transistor amp. I need to tell you that the later versions of "solid-state" amplifiers will sound better than the older transistor amps and that is just due to the newer technology of MOS and FET transistors compared with the "older" bi-polar transistors. Remember I wrote that the FET / MOS transistors are mimicking the Tube rectifier closer and as such the overtones or harmonics are more equal.
Ah, a new word... "overtones". An overtone is the notion that a note can and will sound differently if there are more or less " overtones". Back to the steel guitar. A steel guitar produces lots of "overtones" so much in fact that using new strings makes the sound really bright and almost out of control or un-manageable and many steel players like their strings a bit "dull" or used at least I did on my twin neck Emmons. They way I see it; the overtones are the harmonics you can hear, generally 2nd and 3th harmonics. Some people "hear" 4th and 5th harmonics in combination with the natural tone and that creates the tone they are looking for. So a steel player for instance does NOT want the amplifier to "color" the tone / sound . They do that with the picking position and the hand, palm and the wrist control (complicated he ??). Check out guys like Buddy Emmons, Paul Franklin , Loyd Green, Maurice Andersen and guys from that era. For me, the best out there is Jaydee Maness, who happens to be a good friend of mine.Check him out, he is the guy that plays on Stearway to Heaven by Eric Clapton. He also played backing on The Dukes of Hazzard for about 7 seasons. He is one of the great session players of all times. Check him out at www.jaydeemaness.com . So a steel guitar amp needs to be clean with lots of "headroom". headroom is the idea that you can play MUCH louder without the sound going into distortion. How do you do that ... well. there it is, you need a BIG transformer to drive very high voltage to the transistors. Amplifiers are really specifically made for that; Evans, Shobud and Peavey are some amps that work well for that purpose. In the 60's the favored amp used to be the Fender Twin because it could stand the abuse and had the power needed to cut through the band but that changed when Peavey came on line with their Seesion 400 and Session 500 models with a HUGE 15 inch Black Widow speaker. A quick remark here, we used to change the 2 x 12 JBL's out for a single 15 inch Black Widow in the Twin because we kept blowing the JBL speakers. The Black Widow speaker does not blow. It least in the combo with the Fender Twin it did not blow the speaker.
So, when you look at a normal 6 string guitar, very few people have the skill to change the sound with their hand / fingers thus they rely more on an amplifier to provide that function and remember, the overtones or harmonics provide this creamy sounds that really goes into overdrive without necessarily increase the volume accordingly hence the preference for the bottles (tube rectifiers) . Remember, the measure of " loudness" is db or Decibel and it's a logarithmic number ie to double the volume (loudness) the db number only increases by 3. As an example, 90 db is twice as loud as 87 db.
That's it for today.
More useless information for you'all. One of my good friends actually was the engineer that, in the early 60's, build theVox amplifiers for the Rolling Stones and the Beatles in Dartford, England where the VOX factory was situated. He is now one of the big boys at JBL ( Harmon as we all know it) in Los Angeles. These Monsters amplifiers had 30 Watts ( AC 30) and later they even had some amplifiers that had 100 Watts.!!! ( smile) The Beatles played the Wembley stadium with that kind of amplification.
Enjoy reading.

My current list is:

1962 Fender Twin reverb with a 15 Inch Black Widow
1975 Sho-Bud Twin Christmas Tree
Evans Steel guitar amp large cabinet with 15 inch JBL
Evans Steel guitar amp small cabinet with 15 inch JBL
Fender Blues Junior - modded
Fender DEC -30