It seems after committing code to the local repository, every programmer will run the command.
git push origin master
to push the local file to
It is not different with client/server model except a local copy, so why is it called a "distributed" one?
In the diagram below alice and david can interact because the system is distributed.
Notice how, say, alice and david can interact because each can act as a server.
Here the dev team only interacts with the main server.
Traditionally speaking source control systems were designed as server-client setups, loosely speaking. So the repository was centrally located.
With git and Mercurial, the system is designed to put all users at equal footing. Everyone has the full repository with them. The control and repository in that way is distributed amongst it users.