Back in my day, drives did not come with the drive "brains" (i.e. controller card) as part of the drive assembly. Hence, a low level format was needed to allow the controller card to write the sector id's, sectors per track and sector interleave to the drive. It basically set up the drives logical geometry, i.e. heads, sectors per track, and # of cylinders. This was also based on the encoding method employed by the controller, be it MFM (Modified Frequency Modulation) or RLL (Run Length Limited). Of course you had to have a drive that could handle the RLL encoding scheme or you would have lots of drive errors. Some MFM drives did work with RLL encoding, however I digress.
So now enter the age of IDE (Integrated Drive Electronics). Drives now had the controller built onto the drive itself, and thus the low level formatting as we knew it was done at the factory and is not done again. In fact, the drive simply takes the INT 13 low level format call and simply "zeros" out the sectors on the drive. No actual "low level format" in the true since of the word takes place. Thus, a drive of today only needs an OS format, or what is known as a "High level format"
That's it in a nutshell. There are more details, but you get the point.