It's explained in great detail in the docs, but I'll try to summarize:

  • matching means git push will push all your local branches to the ones with the same name on the remote. This makes it easy to accidentally push a branch you didn't intend to.

  • simple means git push will push only the current branch to the one thatgit pull would pull from, and also checks that their names match. This is a more intuitive behavior, which is why the default is getting changed to this.

This setting only affects the behavior of your local client, and can be overridden by explicitly specifying which branches you want to push on the command line. Other clients can have different settings, it only affects what happens when you don't specify which branches you want to push.