It guarantees that the text you are seeing really comes from that website, that it hasn’t been tampered with by an actor between you and the server.
This means that Internet service providers and others between you and the website cannot insert ads in web pages. It also means that if you’re reading a newspaper online (for example), you can be sure that the articles you read really are from that newspaper, that all the articles are there and that they were not modified.
It also prevents URL or content-based censorship, since mans-in-the-middle cannot know what URLs you visit or what content you received from a website.
It does not prevent domain name or IP-based censorship, since the man-in-the-middle can know these, and it is also sometimes possible for a man-in-the-middle to know what page you are visiting by examining the length of the URL and content and comparing them with public information available on the website.
It guarantees that the text you are seeing really comes from that website, that it hasn’t been tampered with by an actor between you and the server.
That's what subresource integrity is for. (http://www.w3.org/TR/SRI/) Links with subresource integrity include the hash of the content to be delivered. Subresource integrity allows caching by content delivery networks and ISPs without allowing them to change the content.
Using HTTPS for general static content is that it breaks caching and CDNs. Because it breaks CDNs, many CDNs (especially Cloudflare) break HTTPS by terminating the HTTPS connection at the CDN. They may or may not encrypt from the CDN to the actual host. This makes big CDNs a central point of attack for snooping purposes.
While this is an unpopular opinion, I consider HTTPS Everywhere a form of security theater. We need really strong security on logins, financial data, and such. We do not need to encrypt newspapers or public cat videos.
Transport Layer Security guarantees, among other things, that the content really comes from the server it should come from¹. This means that the content was not manipulated by a man-in-the-middle.
However, it does not guarantee that the content was not manipulated by an attacker with access to the server. If a web application (say Gmail) includes a JavaScript library (say jQuery) served by a content delivery network (say code.jquery.com), it can use subresource integrity to have the browser verify that the library was not manipulated by an attacker.
This prevents the threat model where the content delivery network becomes compromised and an attacker replaces the library by malicious code that sends the private data of users to the attacker.
Subresource integrity can also prevent other attacks, but it complements end-to-end encryption. It does not replace it.
¹ This assumes that the certificate is valid, of course. There are problems with the current certificate authority model, but there are also solutions to these problems.
This means that Internet service providers and others between you and the website cannot insert ads in web pages. It also means that if you’re reading a newspaper online (for example), you can be sure that the articles you read really are from that newspaper, that all the articles are there and that they were not modified.
It also prevents URL or content-based censorship, since mans-in-the-middle cannot know what URLs you visit or what content you received from a website.
It does not prevent domain name or IP-based censorship, since the man-in-the-middle can know these, and it is also sometimes possible for a man-in-the-middle to know what page you are visiting by examining the length of the URL and content and comparing them with public information available on the website.