If you want to allow another developer or user should be able to update files and folder to your repository than you need to add a new collaborator. As a collaborator a person can commite and push the files to your repository.
Here I am showing how you can do it:
1) Log in to your gitHub account and go to your projects.
2) From project list, select the project which you want to share.
3) Click on "+" icon near to profile link on top right corner of page and select "New Collaborator".
[caption id="attachment_928" align="alignnone" width="300"] GitHub-myproject collaborator[/caption]
4) On the page,Â start tying name / username of the person you want to share the files. As soon as you start typing in text box it will show you list of users start with that alphabets.
[caption id="attachment_927" align="alignnone" width="300"] GitHub-Add_collaborator[/caption]
5) Select the user and click on "Add collaborator" button. You can simple delete it by "X" sign if you want to remove it from the list.
That it is. Now user is now able to committe and push the file to your repository.