There are several different formats of film. 35mm is the most common and easiest to use because of its wide adoption. There is 120 Role film where each frame is 70mm, which is double the size of 35mm. then there 8x10 Film which as the name suggest is 8 inches by 10 inches.
Why different sizes. The answer is image quality. 35mm film has a higher range and more depth in colors than digital. But 70mm has an even higher range than 35mm.
With 120 there are higher range in darks to light. you could take a photo of a black statue with white clouds in the background and still get the definition of both the clouds and statue. with Digital you would get blown out white for the clouds and a black silhouette for the statue. the other advantage is that even though the grain density is the same as 35mm there is double the area of grain. this means that if you enlarge a 70mm to a 8X10 it will look twice a clear as the 35mm.