git push doesn't push all of your local branches: how would it know which remote branches to push them to? It only pushes local branches which have been configured to push to a particular remote branch.
On my version of Git (1.6.5.3), when I run git remote show origin it actually prints out which branches are configured for push:
Local refs configured for 'git push':
master pushes to master (up to date)
quux pushes to quux (fast forwardable)
Q. But I could push to master without worrying about all this!
When you git clone, by default it sets up your local master branch to push to the remote's master branch (locally referred to as origin/master), so if you only commit on master, then a simple git push will always push your changes back.
However, from the output snippet you posted, you're on a branch called develop, which I'm guessing hasn't been set up to push to anything. So git push without arguments won't push commits on that branch.
When it says "Everything up-to-date", it means "all the branches you've told me how to push are up to date".
Q. So how can I push my commits?
If what you want to do is put your changes from develop into origin/master, then you should probably merge them into your local master then push that:
git checkout master
git merge develop
git push # will push 'master'
If what you want is to create a develop branch on the remote, separate from master, then supply arguments to git push:
git push origin develop
That will: create a new branch on the remote called develop; and bring that branch up to date with your local develop branch; and set develop to push to origin/develop so that in future, git push without arguments will push develop automatically.
If you want to push your local develop to a remote branch called something other than develop, then you can say:
git push origin develop:something-else
However, that form won't set up develop to always push to origin/something-else in future; it's a one-shot operation.