While I'd mostly agree with the 2 previous answers, here's my take on it.
The term “user experience” was coined by Dr. Donald Norman, a cognitive science researcher who was also the first to describe the importance of user-centered design (the notion that design decisions should be based on the needs and wants of users).
As Jacob Nielsen and Don Norman defined it:
The first requirement for an exemplary user experience is to meet the
exact needs of the customer, without fuss or bother.
To quote the same SmashingMagazine article:
We (UX designers) made design decisions based on just two things: what we thought was
awesome and what the client wanted to see.
We built interaction based on what we thought worked — we designed for
ourselves. ... There was no science behind what we did. We did it because the results looked good, because they were creative (so we thought) and because that was what our clients wanted.
This is what I'd call "Opinion-based design". It is basically you sitting there (ideally with some user observation or market data), making your best guess about what the user's model is and try to match it with your design.
The problem is the reality is just much more complex and rich than what UX designers could have expected. How can we be sure that our design really delivers what the users really need? How does our opinion-based design face against the reality?
There's only one way to figure it out: Trying to get some facts! How?
One way is running A/B, usability testing, conducting user experiments, collecting statistics, gathering usage data (e.g. number of clicks, task completion time, conversion rates, which feature is used, more or less than which feature, etc.). They are some of the "objective" (called "quantitative") methods (trying to collect hard numbers).
The other way is more "subjective" ("qualitative") with user interviews, focus group, surveys where we ask users to report what they thought or think. Even though it's commonly known that the users don't really know what they want or feel, their self-reported data are still a valid measure to take into account.
This is what I'd call "Fact-based analysis". Both methods basically give UX designers some facts to analyze, and rely upon to further iterate the design, and make them better, the so-called "Fact-based design".
We use opinions to create a design, gather facts about the design in the real-world, then use these facts to form some other opinions, then iterate. And on goes the circle.
Hope it helps.
PS: UX is a relatively new field, at least compared to many other disciplines. Consequently, its definition is still very much open for discussion, refinement and even debate. And everybody is kind of having his or her own view on what UX really is, its ultimate goals (e.g. satisfying users/ increasing usability, efficiency, ease of use, etc.), what it measures (from concrete, objective measures e.g. task completion time, to more subjective measures such as user perception or feelings, etc.), its scope (how it relates and whether it includes/spans/crosses the other fields such as HCI, usability, design, cognitive psychology, accessibility, etc.), where its root was, so on and so forth.
So in short, even the definition of UX you heard in the meet-up is still up for discussion :) I'd say that UX is about the full circle between opinion and facts, not just one-way transformation