My understanding of the attack:

Suppose the target web server has an endpoint /foo?probeMe=bar such that the HTTPS response will include 'bar' in the HTML. (Quite an assumption, sure.)

Suppose the target web server compresses its responses.

Suppose the attacker can make requests to the target web server, on behalf of the target user (e.g. when the target user is on an attacker-controlled webpage, and the attacker can make AJAX requests to the target web server).

In the case that the HTTP response already contains 'bar', and doesn't contain 'cbs', then a HTTP response to /foo?probeMe=bar will have a shorter length, than a HTTP response to /foo?probeMe=cbs , since compression will mean 'bar' is deduplicated.

Using this, the attacker is able to mount an Oracle attack. That is, if they know something of the form *@gmail.com , and they want to know the whole email address, they can make 26 probes, with probeMe set to: a@gmail.com, b@gmail.com, ..., z@gmail.com

and whichever produces the shortest response is part of the response.

Suppose the shortest is the probe for probeMe=y@gmail.com . They try another letter: ay@gmail.com, by@gmail.com, ..., zy@gmail.com . Again, one probe will have a shorter response than the rest.

They continue, until they find larry@gmail.com .

Now they know larry@gmail.com appears in the response. Success!