ASCII and binary
OK - we now have these bits and bytes.
Think about a byte - 8 on/off switches in a row. There are 256 possible combinations of on/off switch combinations. ( I highly suggest a textbook or website with some good graphics here to help with this explanation)
OK, now, what do we do with these 256? There are two options, really: binary and ascii.
Binary. Counting. 0-255. 8 bit data. For example, this is what Landsat TM satellite imagery comes in. Every cell has a 0-255 value. Each cell, therefore, requires 1 byte of storage. For all practical purposes, this data is strictly numeric and limited to 0-255.
ASCII. Each of these 256 values represents a single character. For example, each letter has it's own byte representation. And capital/lowercase letters have different ascii representations. This is why some programs/computers are 'case sensitive' - upper and lower case letters are stored differently.
Now a comparison. How much space would storing the number 111 take in ascii/binary? Well, the number is less than 255, so it would take only 1 byte in binary storage; in ascii, there are three characters, so it would take 3 bytes. Thus, binary is much more efficient - if you limit yourself to 256 values.
A quick google search will give you more websites than you could count for a greater explanation of ascii and binary. Wikipedia has extensive pages on both.