Medium format film is larger (often significantly so) than 35mm film, and is wound onto reusable spools. While 120 is the most common medium format, there are others available, including 620, which is the same size as 120 but uses smaller spools. Medium format film uses a paper backing to protect it from exposure to light, and should be loaded in subdued light conditions.
Typical medium format film is usually in widths of 60mm. The format was determined by how much length was recorded for each shot. That is to say a roll of 120 could have shots in a series of 6x4.5cm, 6x6, 6x7, 6x9 or even 6x12 depending on the camera. 120 and 620 are nearly identical except in the spools, it is quite possible to re-spool 620 film onto a 120 spool, or vice versa as shown at Respooling 620. Now it is quite possible to get into medium format photography very cheaply. Medium format film can resolve enough detail to rival even current digital cameras when scanned on even cheap flatbed scanners, due to their recording area. Two articles that may help in researching medium format cameras on a budget are : Folding cameras on a budget and Twin Reflex Cameras on a Budget.
Currently the two most popular formats are 120 and 220. 120 film is basically a spooled paper-backed film, that will take from 8 to 16 exposures (6x9 to 6x4.5). The paper back typically has rows of numbers that lines up with the (usually red) window on the back for the format of that particular camera. 220 film is the exact same film, except instead of a paper backing, it has a paper leader. The film itself has no paper backing and is twice the length of 120, so instead of 8 to 16 exposures you may get around 15 to 31 exposures. 116 or 616 type film was a 70mm wide paper backed film, which is no longer readily made.