ProtonMail uses OpenPGP internally. What this means is that mail between ProtonMail users is end-to-end encrypted and cannot be read by anyone else, including ProtonMail. In contrast, reading your mail is sort of the point of Gmail, Yahoo, Outlook, etc.—it helps them build advertising profiles of you so that you can be advertised to in more targeted (and lucrative, for them) ways.
From a security perspective, it means that a database breach at ProtonMail would not leak your mail content, whereas it would at almost any other provider. This is also true for mail from outside ProtonMail, as we encrypt incoming mail on your behalf and throw away the plaintext as it arrives. This means that your mailbox acts as sort of a document vault that only you can read.
Finally, ProtonMail also has some neat features that can be used when, for instance, you are asked to email something sensitive to a third party who doesn’t use ProtonMail. In that case, you can set a password on the email and the recipient will receive a link asking them to log in on our secure server to access and decrypt your message/attachments. I’ve used this several times when asked to send documents to banks, etc., and it is MUCH more secure than regular email for this purpose.