When you log in to a computer, you start up your laptop and enter any passwords needed to use your programs and access the internet. When you log in to play Vocabulary.com, you need to type in your username and password.
You can use the terms log in or log on, or even sign in, but whichever way you say it, you're going through the necessary steps to start using your computer or database. At work, you might need special passwords or procedures to log in, while at home you might simply turn your computer on. Log in has been used in computing since 1963, when it was modeled on clock in.