When you send an email to yourself (for example firstname.lastname@example.org to email@example.com) using HTTPS and a web browser, the email is not transmitted out over the internet "in the open". So someone would have to compromise either your computer or the Gmail servers to read your message. However, if you send the message to a different server, such as yahoo, hotmail, or mywebsite.com the message is transmitted across the internet and potentially vulnerable to interception.
Typically no one is going to intercept these emails so if you are concerned only about personal privacy (like the details of a relationship) you don't need to worry. However, if the information is very secret, politically sensitive, or very valuable (like the password to your $5 million Swiss bank account) it is good practice not to send this information in an email because it could theoretically be compromised. A tool such as GPG can be used to encrypt this type of information, or it can be sent by another trusted method.