If I read this right, "hermeneutics" is the science of interpretation; and "continuity" would refer to interpretation of the Scriptures leading to a smooth transition of doctrines of the past into the future without abandoning understood and accepted dogmas.
You're as close as it could be to being correct without a good understanding of modern Catholic history...and the latter is not your fault at all (not being Catholic).
Essentially, there was a school of thought in a lot of Catholic circles that stated that the Second Vatican Council completely redefined what the Church was. This school of thought (the "Bologna School") believed in what was called a "hermeneutic of rupture" -- that is, any belief or any practice that was said or done prior to Vatican II was no longer valid and that there was a compelling need to re-define everything.
Pope John Paul II and, more strenously, Pope Benedict XVI rejected that hermeneutic, stating, instead that Vatican II must be interpreted in light of and in cooperation with all prior Church councils (this "hermeneutic of continuity").
The difference between the two camps certainly impacts how Scripture is interpreted, but it also impacts EVERYTHING...from fundamental theology and dogma to sexuality to social doctrine to liturgy even to church architecture.
I hesitate to do so, but one example of this is that after Vatican II, in many parishes (including my own), altar rails were removed separating the sanctuary from the nave. Believe it or not, there is a theological reason for those altar rails to exist (in the Churches of the east, they have something called an iconostasis that serves the same theological purpose...going back several hundred years in the west, we used to have something called a "rood screen"...which was subsequently supplanted by the altar rail)
A Greek Orthodox iconostasisThe traditional liturgies are formed around the book of Revelation, particularly Revelation 5 & 6. If you look at that, I think the purpose of the iconostasis / rood screen / altar rail becomes pretty apparent. (We are, as St John did, looking upon those events with adoration)
By ripping out the altar rails from churches (because they wanted a "rupture" from the past), they have removed a visible reminder of the theology behind the liturgy. Then, in conjunction with many of the radical changes that they made with the structure of the liturgy itself (many of which went radically farther than what was actually authorized by the Church), it starts to transform how people think.
And then this change in thought starts to spill over into how people think in other areas as well.
Not being Catholic, you may or may not understand what I'm trying to get at...nor will you likely agree...but that is FWIW
Why this is a big deal is that the secular (and left-wing Catholic) media were trying to paint Francis as being on the side of the "hermeneutic of rupture" -- this was something that was causing no small amount of consternation among the more conservative / traditionalist people within the Church. Rather than reading and listening to the actual words of Francis, they were paying more attention to the media spin about Francis (I have been saying for months that they are trying to "create a Francis in their own image").