When you sign up for this type of e-mail account, you are given a username and password to use when logging on to a web site. There are a number of places where you can get free web-based mail. They are doing it so that they can sell you to advertisers, either by displaying banner ads to you, or by collecting demographic information, which along with your e-mail address, they may sell to other advertisers.
Configuration is easier for web-based mail.
In most cases, all that's needed is to remember the userid and password. Everything else is handled by the programmers on-site. Software updates and security problems are handled by the site, too. Depending on your skills and diligence in performing updates and maintenance, it may be better to let Hotmail or Yahoo do these things for you. Of course, since this is all free, it may be the case that you are getting what you pay for.