"Web-based" email means that your Yahoo! Mail account is actually a web site. Since it's online, you can use it side by side with other sites without leaving your browser, and it's accessible from any Internet-connected computer in the world.

"Client" email refers to an email application that's actually on your computer, not on the Web— applications like Microsoft Outlook, Eudora, or Netscape Mail.

Client email applications like these require you to enable the Yahoo! Mail POP access feature to access your Yahoo! Mail account from the client. It's "on" by default, but you can check your POP status by clicking "Options" in the upper-right corner of the screen, then under "Management," click "POP Access and Forwarding."