During web development tasks, you may want one server for email and one for the actual hosting.
As soon as you update DNS nameservers, all email and website data should point to the same web host. Then, all email accounts and files can be managed from there.
But, if you want email on one server and files on another, you need to change the mx data on the server which hosts the actual website. The company that will be used for the email account will supply mx data. You take that data and update the mx data on the hosting website. Then, you go back to the email provider and update the MX data. Now, email service is taking place with one provider and web hosting with another.