This HydrogenAudio article explains secure ripping fairly well:
http://wiki.hydrogenaud.io/index.php?title=Secure_rippingIt comes down to this: Secure Ripping ensures that the data you ripped was bit-for-bit identical to the data that was originally on the disc. AccurateRip is an online database that ensures that your rip matches those of other people.
So, in theory, the only thing that AccurateRip can tell you that ripping in secure mode does not is whether you have a counterfeit source disc (and, even then, a counterfeit that was remastered or something from the original). That's crazy. And, it has issues... False positives are common. Online databases can easily be poisoned by bad user data. And labels sometimes produce discs with minor variations (for different regions or whatever) that will show up as inaccurate, when in fact the audio data on them is identical.
If you search for it on the forums here, you'll find all sorts of discussions about the merits (or lack thereof) of that system. In any case, JRiver doesn't believe it to be a worthwhile feature and it isn't likely to be added to MC anytime soon.