Login and logout is strictly enforced in Linux (Unix systems as well). Unlike DOS/Windows which basically allows one user to have exclusive use of the system, Linux (and Unix) is a multiuser operating system, meaning that more than one user can use (or logged into) the system at the same time. To login, you should have an account in the system and a valid password. Most of the time, when you type password, no "*" is shown on the password field, as if you are not typing anything at all. Again, password is case-sensitive too!
After you completed your work on the system, you should have a good habit in logging out the system otherwise, you risk your personal data. Moreover, bad people may use your session to do evil things! Remember to LogOUT!!!