It's not so much that they occupy more space than they need to, it's that they are literal copies of your work. There are many different forms of compression that may be used, but a VERY simple example is as follows:
Let's say you have a database file that has 5, 30 character fields for the address, and 100 records. When you save the file (ignoring overheads) the file will take 5x30x100 bytes of storage regardless of whether the fields are blank or not - i.e 15,000 bytes. Now assume that 50% of the content is just blank. If we replace all the groups of contiguous spaces with a number to indicate how many there are, followed by a symbol to indicate space, we can reduce the size of the file. So 20 spaces which would take 20 bytes becomes (say) 20{ = 2 bytes.
The disadvantages are potentially threefold. First, if we copy the file to another system which doesn't know the compression method used, then the copy is useless; second, it takes time to perform the compression and decompression; third, the database program probably can't work with the compressed file, so the file will need to be completely decompressed before use, then re-compressed again when it has been closed.