The verb "log on" refers to the process of accessing a secure computer system or website. When you log on to a system, you provide "login" information that authenticates you as a user. This information typically includes a username and password, though some logins require extra information, such as a PIN number or a correct answer to a security question.
Most computer systems can be configured to require users to log on before accessing the system. For example, both Mac and Windows systems can be set up to require all users to enter a username and password each time the computer is restarted or woken up from sleep mode. Similarly, when you access a remote system through a remoteaccess or FTP connection, you may be required to log on to the system.
When you create an account on a secure website, you are typically required to log on to the site each time you want to access your account information. Examples include online banking websites, social networking sites like Facebook and LinkedIn, online Web forums, and a variety of other sites. Any website that allows you to create a unique user account will require you to log on in order to access your personal information. The only time you may not have to log on to one of these sites is if your login information has been stored in a cookie by your Web browser.
NOTE: While the terms "log on" and "login" sound similar, they have separate meanings. "Log on" is a verb and refers to the process of accessing a secure system. "Login" is a noun that refers a user's login information, such as a username and password combination. However, the phrase "log in" (two words) is an acceptable alternative to "log on," and the two terms can be used synonymously.