To say that something "has so much going for it" (or the alternative "has a lot going for it" -- "going for it" is the key phrase here) is to say that it has many (or very strong) positive qualities or that it is in positive circumstances.
What positive qualities or positive circumstances are associated with the thing you're describing depends on the context. For example, if you said,
"Harry has so much going for him when it comes to romance,"
you might mean that Harry is intelligent and handsome.
If you said,
"I'm not sure which job offer I'm going to accept, but the manager position has a lot going for it.
you might mean that the manager position has more attractive pay and hours.
The "positive qualities" meaning is appropriate in your example:
Initially condemned as heresy, this elegant idea had so much going for it that the biological world has long since accepted it."
"It" refers to "idea." The meaning is likely that there were many reasons to support the idea or that the evidence was too convincing not to accept it. "So... that" is another construction interwoven with the "going for it" phrase, so the "that" isn't really part of "going for it. You could rephrase the sentence, "This idea was so convincing that the biological world has long since accepted it."