I want to compress Local Disk C. What effect will this have on my computer?
To compress means to makes the files smaller. This can be done in several different ways.
Is it a good idea? Personally, I think it's a very bad idea. It can make your computer slower, and most import, it means that a disk error can cause the loss of everything on the dive, rather than just a single file.
If you are short of disk space, I highly recommend buying a bigger hard drive. They are not expensive.