A Decompression Bomb is a compressed-format file that expands to fill your disk when opened.
For example, using GZIP to repeatedly compress a specific byte stream in three stages can result in a file of only 5928 bytes that when expanded is 100 gigabytes! Other file formats that use compression are vulnerable as well, for example a GIF file that represents a 6000 x 6000 black rectangle compresses down to 25527 bytes but will expand to over 100 megabytes when represented as a 24-bit image.
The bomber sends you an email with a compressed attachment designed to choke a virus scanner or the like.
Don't open them unless you're sure about their source! If downloaded with p2p software you should be really carefull with these files. I suggest you delete them asap.