If your domain has more than one MX record, the mailer has to figure out which one to use. MX records use a field called preference to determine the priority. When you create an MX record, most DNS hosting providers require you to set the preference number. Some label the box preference, and some label it priority. Some require a number, and some ask you to select Low, Medium, or High.
If you only have one MX record, any value is fine for priority or preference. However, if you have more than one MX record; for example, if you use an MX record to verify that you own the domain, as well as an MX record used for mail routing, make sure the MX record for mail routing is higher priority than the one used for validating that you own the domain.
Mail is delivered to the mail exchange server with the lowest preference number (highest priority), so the MX record you use for mail routing should have the lowest preference number, typically 0. For example, use 0 for your mail routing record, and 10 for the record for validating that you own your domain. Or, if your DNS hosting provider uses Low, Medium, and High, use High for your mail routing record, and Low for the record for validating that you own your domain.
Specific directions are included in the step-by-step instructions for popular DNS hosting providers.