This is almost but not exactly what the sentence means:

Since a BigInteger or BigDecimal contains more bits than an int or float, the operations on a BigInteger or BigDecimal are slower than the corresponding operations on an int or float.

Searching for an elided noun

If you pretended that the word "bits" had simply been elided, then you'd have this:

Since there's more bits involved, the operations will be slower.

But that's ungrammatical, since the plural "bits" doesn't agree with the singular "there's".

Really, "more" refers not just to the greater number of bits that can be in a BigInteger or BigDecimal, but also to the additional computation required to manage the variable number of bits in a BigInteger or BigDecimal.

The singular "there's" suggests that the author wants you to think of "more" as modifying an unstated mass noun.

There is no elided noun—and that means something

You could understand the sentence like this:

Since there's more stuff involved, the operations will be slower.

as if "stuff" had previously been said, and is now elided in order to avoid repeating it. The odd thing here, grammatically, is that there is no elided noun. "Stuff" was never said, nor is there any word that refers to the number of bits and the computational overhead.

Using the grammatical construction for an elided noun modified by "more" when no such noun exists is a common way to communicate vagueness in English. It would require a lot of words to try to explain in detail what "more" modifies. That would probably distract from the author's main point, which is the trade-off summarized in the next sentence. Probably the text explains the details elsewhere. By omitting the noun, the author is essentially gesturing vaguely to the unstated messy, complicated "stuff" that he'd rather not try to name. The word "stuff" is probably too informal for the tone the author was trying to convey. But "more involved" without a noun is acceptable formal English and means the same thing.

Grammatical stuff

One could argue that "more" is a pronoun, referring to what was previously talked about. But one would meet the counterargument that a pronoun stands for a noun, and there is no noun. (One could argue back that "more" is a dummy pronoun, like "it" in "It's raining", which doesn't stand for a noun, but one would meet disbelief.)

One could argue that "more" is a noun here: "there's more involved", analogous to "there's diplomacy involved". But one would meet the counterargument that "more" is clearly modifying something. There is more of something involved. The grammar of the sentence is analogous to "Twenty people have arrived and we're already out of chairs. Since there are more [people] coming, some [people] will have to stand." That's how a listener understands it.

Or one could avoid arguing about terminology, and see the approximate truth in both of those theories. I think that what's really happening is just that the "more [elided-noun] predicate" construction is familiar enough that people can use it and be understood even without a real elided noun, without upsetting a listener's need for grammatical coherence, as long as the context supplies a meaning (not necessarily a word) for the non-existent elided noun.

There is an implied back reference there. Read it as:

"there's more involved with using a BigInteger as opposed to an int"

The author is assuming the reader will know he's is referring back to the BigInteger vs int question.

BigInteger is a structure while int is a primitive so using or manipulating a BigInteger requires more cycles.

I personally don't see anything wrong with it. I suppose the noun is implied, for example:

There are more operations involved.

There are more calculations involved. etc.