"abstraction over type constructors" isn't very meaningful without more context anyway, but they're probably referring to something like the following:

non-abstracted:

    map :: (a -> b) -> List a -> List b

abstracted:

    map :: Functor f => (a -> b) -> f a -> f b

"List" is a type constructor (it takes a type and returns a type), but we can write a "map" function that works over more types than just List - for example, Maps and Options and so on (aka "Functors" in Haskell parlance). We've "abstracted (the function map) over the type constructor (of the data structure being mapped over)".

To answer your more general question, if you just learn functional programming on a language with a powerful type system (Haskell is probably the most germane example) you will learn at least some of these terms. Most of them turn out not to be very deep, just hard to explain (for reasons unclear to those who understand them), but still very useful.