Webmail allows you to manage your emails in a way analogous to what you do using software such as Outlook or Thunderbird. However, this is done through the application running directly from your browser and on any computer with Internet access. It is important that you log off when accessing your mail on public computers so that others can not access your email account.
You can check the webmail of any account by logging into "http://webmail.yourdomain.com" with full username (firstname.lastname@example.org) and password for the email account.
To check your email through a mail client (Outlook, Thunderbird) you will need to configure the application. Your most likely email server is "mail.yourdomain.com". You will need to use the complete user (email@example.com) and password when setting up your account in your mail client. You must also check the "My Server requires Authentication" option.