Pushing: conflicts and what to do when it is rejected

A commit lives on your machine until it is pushed. Pushing is a separate action, and it can be rejected: that means the shared history has gained something you do not have.

git push origin master   push
git pull --rebase        take theirs and put yours on top
git push origin master   try again

A conflict is not a breakage but a message saying "two people edited the same place, decide which is right". You open the conflicted file, keep what is needed, remove the markers and make an ordinary commit. The more often you pull, the more rarely this happens.