Webmail is email client implementation as a web application running on a web server. It provides basic functions such as receiving and sending email via web browser.
Basically, there two types of webmail: (1) a webmail software that can be downloaded and installed to any webserver or (2) a webmail that provided and maintained by ISP/Free Mail Provider.
Some examples of webmail software were roundcube and squirrelmail. It must be downloaded, installed and configured by sysadmin so it connected to existing mail stack. End user can access the webmail after they provide username and password.
Some examples of webmail provider is Gmail, Yahoo and Hotmail. All of them are free to use. They also provide the paid version of webmail with more advanced functionality.