A mail client is a program used so that you can download your email from the server and retain access to it without having to access the server directly. To put it simply, a program like Microsoft Outlook is something that is installed on one computer. When you configure it with your Business Gmail, Outlook will go online and download your emails so that you may view them and manage them through Outlook. You may still access your email anywhere you have internet access, but it will require you to login directly to the server.
Google has detailed instructions on how to set up your email on almost all mail clients.
IMPORTANT: When setting up your email, you normally will have two options... POP or IMAP. You can set it up either way, but please read this explanations before setting it up.
What's the difference between IMAP and POP?
Unlike POP, IMAP offers two-way communication between your web Gmail and your email client(s). This means when you log in to Gmail using a web browser, actions you perform on email clients and mobile devices (ex: putting mail in a 'work' folder) will instantly and automatically appear in Gmail (ex: it will already have a 'work' label on that email the next time you sign in).
IMAP also provides a better method to access your mail from multiple devices. If you check your email at work, on your mobile phone, and again at home, IMAP ensures that new mail is accessible from any device at any given time.
Finally, IMAP offers a more stable experience overall. Whereas POP is prone to losing messages or downloading the same messages multiple times, IMAP avoids this through two-way syncing capabilities between your mail clients and your web Gmail.
If you're trying to decide between using POP and using IMAP with Gmail, we recommend IMAP.
Supported IMAP client list
Supported POP client list
Mozilla Thunderbird is a free mail client that you may download.