What this means is that there is this whole school of thought that Reb Chaim started that basically says that there is a way to justify the Rambam.
Now to some degree this process started a long time ago, but it just was not very effective. At the most you would get with the Beit Yoseph and others the source from where the Rambam got his law from. But almost never "Why" or "How?"
The אור שמח I think was the actual beginning of this process. But it is mainly attributed to Reb Chaim. The reason I usually mention Rav Shach is that he brought this process to the pinnacle of perfection is his book the Avi Ezri. Or at least that is how it seems to me. My own experience with the חידושי הרמב''ם of Reb Chaim is that it always leaves me unsatisfied. Always. I always end up more confused than when I started. Even though he goes a long way in solving the difficulties with his יסודות foundation principles. Still I always end up with a feeling that things are more confusing than when they started out. But with the Avi Ezri I always feel amazingly happy after I have finished a piece. I feel when he answers a difficult Rambam that the problem has in fact been solved.
[The general Litvak approach does not usually include the Rambam's idea of learning Physics and Metaphysics. I assume the reason is because even to the Rambam there is not question that knowing Shas come first and that is something that takes a certain amount of time. I learned Gemara for years and only recently did God grant me to write two small booklets on Bava Metzia and one on just a few places in Shas.]