When you browse a webpage containing eDonkey2000 (ed2k) links and click on one, your ed2k client starts downloading the corresponding file. The purpose of the ed2k link catch0r is to catch and save these ed2k links when no ed2k client is running - either because there is no client installed on the PC you are using (e.g. at work), or because you shut the client down.
The ed2k links are saved in a plain text file so you can easily copy and paste the links e.g. in order to email them. Alternatively - if you closed the ed2k client, but now have started it again - all the catched links can be added to the ed2k client with a single click.