A repository is a way of storing information related to a file system. For version control software (VCS), it is used to store information about files, their size, date of creation, and any changes made to them (often called "commits"). Common examples of software that use repositories are Git and Mercurial, but others do exist.
A repository can be stored on a person's computer locally (not on the internet), but it can also be stored remotely (on a network or the internet). One of the most popular websites for hosting repositories is GitHub, however others such as GitLab exist. If a person wants to use a public repository on these kinds of websites, they can "clone" the repository onto their computer. This creates a copy of the repository, and all of the files (usually computer code) related to it. A person can then make changes to the repository, and they can "commit" those changes to their local repository (which means that their changes are recorded in the repository's history). If they wish to update the remote repository (the one stored online) they can "push" their changes to it. This updates the repository on the website or network location.