webmail is a email service hosted on a website. This is in contrast to pop3 or IMAP email accounts which requires a separate client application such as MS Outlook or Mozilla Tbird to send & receive email.
a webmail account is nice because you can access it wherever you have a internet connection. Also, you're host always keeps all your email on their server as opposed to the pop3/Imap accounts which download your email to the machine your working at and then deletes the mail off the server. This way some of your email could be on one comp and some on another.
my favorite web mail services are gmail and yahoo. gmail is by invite only and gives you 2+gb of space. i have invites available, pm me if you need one.