A hash is a signature made from a file, and is unique to the contents of the file and not the filename. Because of this you can have the file named whatever you want and search for alternate sources and always get the right file. It also helps to prevent you from downloading an incomplete version of the file you're looking for.
An example of a hash is GZ6Y5XRYFOZ77E2KO55AQ4OT5TN2KCWBJ6RFUFA. That's the hash for the DC++ .401 installation file. If you search for dcplusplus you'll see a column with "GZ6Y5XRYFOZ77E2KO55AQ4OT5TN2KCWBJ6RFUFA" listed. You can also search for the hash itself by setting the file type in the search set to TTH. If the file's not complete the hash would be different, so if you know the correct hash, you can always make sure you're getting the complete file and not someone's partially downloaded version.