MX (Mail Exchanger) records are DNS (Domain Name System) records that specify the mail server responsible for handling email delivery for a specific domain. In the case of Gmail, the MX record is used to direct incoming email messages to Gmail's mail servers.
Whenever someone tries to send an email to a user in your company, their SMTP server does an MX lookup in the DNS to see where to send this message. If that server is not able to find an MX record it won't be able to deliver this email.