Version control systems are self-hosting when they are used to manage the primary repository of their own source code. This shows confidence because if the program breaks, then it breaks its own configuration management, which could be a headache to unravel. For example if the repository format changes, then the change has to be managed so that the old versions remain accessible through the new version of the software. If this is not managed, and old compiled binaries of the version control system disappear from existence, then it may become impossible to recover the old sources.

Thus, successfully self-hosting a version control system is some measure of evidence that the developers know what they are doing and can manage the changes. (And thus they understand change management and we can trust them to be working on version control software.)

http://en.wikipedia.org/wiki/Self-hosting

"Other programs [than compilers] that are typically self-hosting include kernels, assemblers, command-line interpreters and revision control software.

Overloading the term. The OP presumably meant that the source for git was under git source control.

'Hosting' means 'contain', 'serve'. A building can host a department or a convention, and a married couple can host a dinner party, with neither being required to be a webserver or programming language.

To add to that, IMHO self-hosting for VCSs is closer to the original meaning of the phrase than for compilers.

Yes, that's what I meant.