Use the rename operation when you want to change the name of a file or directory. The operation is added to the pending changeset, but the item in the working copy typically gets renamed immediately.
There is lot of variety in how version control tools support rename. Some of the earlier tools had no support for rename at all.
Some tools (including Bazaar and Veracity) implement rename formally, requiring that they be notified explicitly when something is to be renamed. Such tools treat the name of a file or directory as simply one of its attributes, subject to change over time.
Still other tools (including Git) implement rename informally, detecting renames by observing changes rather than by keeping track of the identity of a file. Rename detection usually works well in practice, but if a file has been both renamed and modified, there is a chance the VCS will do the wrong thing.