Registry in a nutshell: The registry is the part of an operating system which records the relationship between hardware, memory space and addressing. It is a database which stores settings and options for the operating system. It contains information and settings for all the hardware, software, users, and preferences of the PC.
As programs are added registry files are created. When programs are removed those registry entries sometimes don't get deleted. Over time the registry can can clogged with useless files taking up space, resulting in performance issues.
To clean the registry is to remove any files that are no longer needed. The best thing you can do is read and understand what the registry is and does and how to back it up. There are apps that will scan the registry and list possible files for deletion.
There are some strange people who know the registry like the back of their hand and know how to hack it for their own devious purposes. I myself am not that geeky.