- In git lingo, most likely they will think about the fact that you don't need a different directory to switch to a different branch.
- In subversion lingo, they will probably mean that the cost of making a branch in the repository does not impose an expensive operation
- In bzr lingo, it seems they mean a repository with short history (aka shallow copy, for most other people)
- it seems that mercurial refers to git's meaning as "named branches" (not sure about this); not sure if mercurial documentation refers to anything else as "lightweight branches"
- for subversion: to create a working copy without any meta information
- for mercurial/hg: "The act of exporting a changeset generates an augmented patch file that describes the change."
- for git, it seems to be a useless 'cp -r' operation
No wonder we have communication problems and people don't grasp the power of a new tool when it changes the meaning of previously used terms.