It’s just saying that
There’s more and less general categories. E.g. “Sunny day” is more general than “Sunny and cool” because if a day is S&C then it’s also C, but there’s also days that are Sunny but not Cool.
Often, if you take two categories, neither one is strictly more general than the other one. E.g. “Sunny and cool” and “Cool and buggy”. There are days that are S&C but not C&B; and there are also days that are C&B but not S&C.
You can take unions and intersections. The intersection of “Sunny and cool” and “Cool and buggy” is “Sunny and cool and buggy”. Intersections give more specific (less abstract) categories; they add more constraints, so fewer possible worlds satisfy all those constraints, so you’re talking about some more specific category of possible worlds. The union of “Sunny and cool” and “Cool and buggy” is “Cool; and also, sunny or buggy or both”. Unions give less specific (more abstract) categories, because they include all of the possible worlds from either of the two categories.
If you want to get more specific, you want to start talking about a smaller category. So you want to go downward (i.e. to a smaller set, included inside the bigger set) in the lattice. But there’s multiple ways to do that. E.g. to be more specific than “Cool; and also, sunny or buggy or both”, you could talk about “Sunny and cool”, or you could talk about “Cool and buggy”.
(This is far from everything that “abstract”, “specific”, “category”, and “concept” actually mean, but it’s something.)
I say “gippity” meaning “generative pretrained transformer” which IIUC is still true and descriptive for most of this, except Mamba.