The standard approach in web applications is to allow new users to register by selecting a user name and a password in addition to providing other information such as email, date of birth and so on. Next time a user visits your web application, they just need to log in using their user name and password combination. So basically it's a two step process: first register (or sign up) then log in (or sign in).
With Yahoo!'s browser based authentication, you can relieve yourself from building a registration component for your web application and relieve your members from having to go through yet another registration process. Yahoo! allows you to authenticate users using their Yahoo! IDs. So you only need to ask users to log in, without ever needing them to register at your web site.