The Merriam-Webster Dictionary defines 'integration' as, "the act or process of uniting different things." In an academic sense, and more specifically relating to teaching mathematics, integration means teaching mathematics across the subjects together instead of in pieces. For example, and integrated 9th grade math course might cover a little bit of algebra, geometry, and probability and statistics instead of simply just Algebra 1 this year and geometry the next.
So why is this important? In the state of Ohio, my licensure is technically labeled as "integrated mathematics," however we are not taught how to teach an integrated classroom. In fact, we're taught how to teach to the traditional standards, despite the Common Core State Standards having an integrated mathematics list of standards. Although there is a point to be made about teaching us how to teach to the standards, shouldn't we also know the differences between traditional and integrated curriculum? After all, the United States is one of the few countries that doesn't teach integrated courses across the board.
To give you an idea of what an integrated classroom might look like, a teacher might teach algebra and geometry in a way that shows the relationship between the mathematical concepts. This often involves teaching concepts in a real-world context, since math occurs in real life across multiple concepts not just algebra here or pre-calculus there.
On the other hand, if the "integrated" mathematics part is supposed to refer to our undergraduate math courses, I'd also argue that we aren't even learning in integrated courses. In fact, they're very clearly laid out as "Modern Geometry" and "Linear Algebra" with 3000 and 4000 level courses.