The subject of web marketing is too vast to handle in stackoverflow.
Gmail can tell you if an account exist because they keep track of bounced emails. Of course, if it's a gmail, they check their own DB.
When you send an email to a non existing account, usualy the receipient server responds with a bounce email to tell you that it doesnt exists.
All web marketing application/email service providers keep track of bounced email because it deteriorates their notoriety, and it goes low enough, future sent mail will end up directly in junk/spam and will not be responded to.
You can track if an email has been opened with a tracking pixel but it's not 100% accurate.
A tracking pixel, is just that, a 1x1 image (often transparent) present on the email that has a link to your server. when the user opens the email, it loads the image via a get request.
For example: <img src="example.com/pixel.php?email=jhon@example.com" />
the scripts return an image, but before that it regiters that the email is valid.
This also can be countered by not loading the images of the email (notice that almost all email service providers ask you to confirm load the images in an email.
The most accurate method is to request an activation from the user at subscription or more commonly named confirm email or double opt in
This requires that the user enters a valid email to be able to continue the registration process. but even here, people can use temporary email (google "temporary disposable email")
TLDR;
You can't tell directly that an email address doesnt exists. (unless you already know that by tracking bounces)