If you want to contribute to WordPress core, you need to have a local install of WordPress on your computer to break, play with, and develop with. A local WordPress install allows you to create/test patches, find/fix bugs, and help develop/test new features during a release cycle.
There are two steps to installing WordPress on your computer for contributing to core:
Installing the latest nightly release from a zip file will allow you to beta test the code, and contribute bug reports. However, if you want to contribute patches along with those bug reports, you’ll need to install a version-controlled copy of WordPress trunk.
SVN and Github are both version control systems. You’ll become very familiar with them when you are contributing to core.
Subversion (SVN) is the official version control system used by the WordPress Project.
For those who prefer working with Git, a mirror of the SVN repository is hosted on Github. Please do not make pull requests, but submit your bug reports and patches to Trac instead.