The main reason why a level should not consist of one big image is that this would require an enormous amount of memory. Therefore one could only have very small levels. However, if you build up the level using blocks, whose size is usually 16 x 16 or 32 x 32 pixels, then you need much less memory. Why? Well, usually one only needs a fairly small number of different blocks and the memory usage per block (that is, for an area of BLOCKWIDTH x BLOCKHEIGHT pixels the player is seeing on the screen) is only a few bytes (min. 1).
The techniques I'm going to describe here are designed for the Amiga Chipset (ECS/OCS/AGA). A very important role is played by the Copper, which makes it possible to code every kind of scrolling one can imagine (horizontal only, vertical only, 8 way scroller) in such a way that you never actually need scrolling graphic data around in memory with the CPU or the Blitter. No matter what you want to do, you just need to blit blocks 'coming in'.
As far as I know, VGA graphic chips, as also used by Amiga GFX cards, have as standard built in all the functionality needed to use the same or very similiar techniques for scrolling: