Live.com is Microsoft’s all in one authentication service where you can register and then use the same credentials for many different things. For example, if you own an Xbox, or have a Windows Live Messenger account, or if you use Hotmail, then you’ll already have a Windows live.com sign in.
Many people like having one single username and password to access services they use regularly. It saves the need to remember multiple passwords, and in this day and age when there seems to be so many different websites needing usernames and passwords to access them, having less to remember is a godsend. A single sign in point also means that once you’ve used your live.com sign in to access one service, you’ll also be able to access all the other services too. Your computer should remember your credentials in its memory, or cache, and not bother you again.