A traditional plumbing system is sort of like a tree with branches. If you need to shut something off, it may not have an individual shutoff and you might end up shutting down the whole house.
With a manifold (generic name) system, they typically run a line from that to each fixture separately (home run). This gives you much easier control, since they (usually) have an individual shut off for each run. It usually is plumbed with pex, and doesn't require any fittings except at the start and the end, so there is less chance for leaks. You can size each individual run for it's load, and because it is smoother without angles and various fittings in between, can often flow more water (but, the inside is smaller than the equivalent sized pipe).