An email client is what you use everyday to send and receive emails.
Is it that simple?
Yes, essentially. Email clients enable you to access your inbox across a multitude of devices; Outlook, Gmail and Hotmail all have apps that allow you to host your inbox on your phone but their basic functionality is still the same. Send, deliver, delete and mark as spam. Just be careful not to confuse them with your email provider. Outlook may be your provider, but Outlook for iOS, Outlook for Windows and Outlook.com are different email clients.
Why is it important to know what your subscribers use?
Rather than optimising your email template for the industry-wide most popular email clients, find out what your subscribers are using. It will save you time and improve their experience of your emails.