How are emails sent?
There are two options for the actual delivery of the emails. The first is that MageMail can send the emails through whatever mail configuration Magento has setup - whether that's the default web server's mail server, or some other SMTP configuration, etc.
MageMail basically just sends the contents of the email over the MageMail API to Magento and Magento sends the email out exactly as it would send a welcome or order confirmation email out.
The second option, which is what most of my customers use, and what I recommend is that you setup a Sendgrid account, drop your Sendgrid API Key into the MageMail backend, and MageMail sends directly over the Sendgrid API.
This is a little bit faster and puts less load on your Magento site.