It's supposed to allow for rapid launches of Pegasus XL rockets. The rocket is supposed to be suspended by a pylon between the two cabins. Once the plane reaches cruising altitude (approximately 12km, 40k feet), the rocket is detached, fired, and boosts ~half ton payload into LEO.
Advantages are: (1) you can technically launch from anywhere in the world with a long enough runway, (2) you can "technically" launch into any orbital inclination, (3) it is relatively cheap to launch a small satellite/payload of ~500 kg into orbit, (4) you can launch relatively quickly and not have to ride-share as a secondary or even tertiary payload on someone else's rocket (and therefore, you are not launching on someone else's schedule).
Negatives are (1) you cannot launch payloads which are heavier than 500kg (technically you can, but the payload just won't reach orbit - lol), (2) cannot launch payloads that are larger than the 1.2m fairing, (3) you are basically limited to LEO (technically you can kick a payload into higher orbits, but it would literally have to weigh just a few kilograms), (4) a human pilot is required to launch a small payload into orbit, which increases the risks of launching.
Generally speaking, it's good for the micro and nano-satellite industry, universities, and scientific institutions that want to launch a small satellite into LEO relatively cheaply, relatively quickly, technically into any orbital inclination, on their own schedule independent of ride-sharing commitments/agreements.
Negatives are that you are limited to how large of a payload you can launch how high, and there is an increased risk for humans due to the requirement of a piloting team for the Stratolaunch system.
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