I'm not highly knowledgeable in security, but the gist is if a block cipher uses the simplest mode of operation (ECB) each block is encrypted independently - good for sync bandwidth but from that the attacker can derive the structure of the file which will help to recover it or it can be used to check if known file in present in encrypted data(watermark attack [1]). More advanced block cipher modes "blend" to some extent blocks hiding file structure information (but if you change single bit a bunch (or all) of the blocks is changed). Also there are stream ciphers, which don't use blocks at all. If you change 1 bit stream cipher will change 1 bit in its output. The problem is it's insecure to use the same key twice with stream cyphers (reused key attack - [2])- e.g. if files with known text is encrypted (think English text, xml files, jpeg headers). Of course it can be overcome by using initialization vector ("seed" which is used with the key), but that IV should be different for each file and you should somehow save it to be able to decrypt it.
Try doing the matasano challenges :). I completed the first two and it was my first exposure to block cipher weaknesses. I had almost zero crypto knowledge before that. All you need to know is programming and basic arithmetic.
How is the best way to get this done, security considerations as against bandwidth?