Don't worry about it, though. You probably won't be using one in your life time. Just get yourself a nice little point and shoot digital camera and you'll be fine
The term 'medium format camera' comes from the days of film and denotes the size of the negative. The most popular film ever is always 35mm (measured as the diagonal of the negative). The most popular medium format was 6x4.5cm. Next up was 6x6cm used predominantly by Hasselblad (you know, the cameras that went to the moon). Mamiya and one or two others use 6x7cm negatives. There is also Large Format!
The main benefit of medium format over 35mm is the larger negative allows you to blow up the picture much further than the 35mm allows before grain and blemishes set in. Furthemore, the medium format cameras were aimed much more at the pro-photographer. Most allowed you to change the film back even when part-used. In this way, the pro could take a few shots with a back containing polaroid film to see the results there and then, and then switch back to alternative film and shoot away. It also meant you could have black and white film in one back and colour in the other, a combination which a lot of nature photographers would carry with them. All of these are features we take for granted with digital of course, since it allows us to make these changes in software. The killer advantage of medium format over digital remains - to this day - how far you can blow up the picture and remain tack sharp. 16 megapixels isn't a patch on the resolution of 6x4.5, let alone the larger formats.
The downsides are that the cameras have to be a lot larger than the standard cameras. The lenses are typically a 72mm minimum and for fast lenses you're talking bigger and heavier. This raises the cost of lenses significantly too since the glass has to be precision ground in order to avoid abberations. A standard lens in medium format is of the order of £500 whereas the equivalent in 35mm would be £200. You also therefore get limited zoom lenses in any medium format range purely because of the cost, size and weight. You usually only get prime lenses.
For many years I lusted after a Bronica ETRSi. I've never bought one, and I still really wish I'd enjoyed the experience, but with the advances and convenience of digital, I fear I'll never give medium format a go.
So back on topic. I've been browsing the MF areas at KEH & the prices of bodies & lenses surprised me...as in they are reasonable affordable in comparison with the fancy DSLRs we're playing with. It's the digital backs that cost a fortune. Then of course, you can go Holga for all of $30 and be shooting MF. I'm sorely tempted....
Minor correction to Frank....and I know.... 35mm produces a FRAME SIZE on film of about 24mm wide and 36mm in length. The DIAGONAL is about 44mm and is considered the 'normal' lens for that format.
Medium format? Much in 120 film....The FILM is blank, so cameras can turn that into 12 exposures of 6cm x 6cm.... Or fewer exposures of 6cm (wide) and 7cm length. I've see at least one camera which did a panorama from the SAME film. 6cm wide and LONG. But few exposures per roll. Lomography, Hasselblad and Fuji made them. I think they' are ALL not only available on the used market. The 6cm size is what's called '2 and a quarter'....or 2 1/4" X 2 1/4" on the negative. The 6x7 is 2 1/4 X 2 3/4 which pleases some who do not like a square format.
Modern cameras CAN stitch INTERNALLY and make one panorama from a panned shot. Even my Cell Phone does that today. The time when I had to slave away in Photoshop to get a result is long gone.