The git push command is used to communicate with another repository, calculate what your local database has that the remote one does not, and then push the difference into the other repository. It requires to write access to the other repository and so normally is authenticated somehow.
Git will normally only allow you to push your changes if you have previously updated your local branch with the latest commits from its remote counterpart. Only when you are up-to-date will you be able to push your own new commits to the remote.
The --force option for git push allows you to override this rule: the commit history on the remote will be forcefully overwritten with your own local history.
This is a rather dangerous process, because it's very easy to overwrite (and thereby lose) commits from your colleagues. Also, even if no one else has pushed anything to the remote repository in the meantime, your colleagues might still have based their new work on the old commit history. Your "force push" changes this history and means theirs is not in line with the new one anymore.