An MX Record (Mail eXchange Record) is a file that explains how email should be delivered to the right address.
There are several kinds of DNS records, which explain to computers how to find the things you are looking for. MX Records are one type of them. When you send an email, the DNS servers first look in their cached files to see if they know where to send it. If they don't, they ask another server which, if it also doesn't know, then asks a third server, and so on. When they find the server that knows, it returns an MX record that explains where the email is supposed to go.
An MX record is the way that these servers figure out where to send your mail as well as how it should be sent. Usually there's one main server and several backup servers, in case there's too much traffic on the main one.
In this way, you can set up your site with us at Thobson Domains but set up your email to be delivered through another service. Even though our email hosting is free with any of our great hosting plans, we understand that you might want to keep using the interface you've grown used to.