A local account controls access to one single, physical computer. Your local account credentials (username, password, and SID/UID) are stored locally on the computer's hard drive, and the computer checks its own files to authenticate your login.
This differs from a network domain account, such as a University account, which is created and stored on a network server (sometimes called a domain controller). Computers query the server for network access.
A local account allows you some level of access to an individual computer. The local account's settings determine your rights for running programs, installing and removing programs, accessing files, and enabling or disabling services.
