MX records (short for mail exchange) is a type of record used to decide where to send emails, and they are used together with A records. They are also sometimes called MX entries. With MX records, you route an email to a specific server when a request is made to a specific domian/subdomain (using the A record). When the sending mail server looks for the recipient mail server, it will look for the recipient server's MX record. The MX record points to the A record, which in turn, points to the mail server's IP address.
You can set up your MX records in many different ways depending on what you want to happen with certain emails. For example, you can have lots of MX records for a single domain to provide redundancy and make sure that the emails are delivered. Some email providers will designate multiple MX records/servers that can accept your email, and then you can set the priority value for each. Servers with lower MX record numbers will be given the highest priority. That means that when a domain receives a request, it will use the MX record/server with the lowest number first. For example, let's say your providers uses values 0, 5, and 10. The MX record with 0 will be used first, then if that mail server doesn't work, it will use 5, and if that mail server also isn't working, it will use MX 10.
You can also set up backup MX records that send mails to other providers. Since these are backups, they are usually given a higher value=lower priority. Most providers show the naked form of the host name (@).