A resonator is an anechoic chamber that deadens sound waves of a particular frequency or all frequencies depending on design.
Resonators, in a vehicle, are used to cancel out soundwaves caused by the exhaust pulsing and cooling within the system. This resonance, aka drone, is inherent in all exhaust systems.
Normally you find them downstream of the muffler at the rear of the exhaust system near the tailpipe, just before the exit. There are some car makers that place a resonator in the system in front of the muffler. The difference between the two boxes is a muffler is pretty densely packed with sound deadening materials and baffles vs. the resonator which is a loosely arranged set of baffles within a metal case. I've seen some resonators that have very little to no baffling and is "tuned" by design of the box to cancel out some specific soundwave frequencies.
Benefits? Quieter exhaust with no drone.
Downside? Quiet exhaust.
Variations? Yes, lots of them. For instance, my car's stock exhaust had resonators and my aftermarket Corsa system has resonators...but it sounds totally different.
Better flow? With a reso delete you'd think the flow would be better but in many cases it really doesn't change. A resonator is not built like a muffler so it really won't impede flow that much. If anything, it helps maintain a certain exhaust scavenging velocity to avoid loss of low end torque.
Pictures - Here's a few that show you a resonator in systems, out of a system, etc...
2007 Ram MegaCab HEMI - from left to right muffler, resonator and tailpipe removed:
2014 Ram CC 6.4L HEMI - First pic, look at the rear wheelwell right behind the tire. You'll see the faint aluminum glint of the resonator at the end of the system. Second pic, an up close shot of the reso. Third pic, reso and tip on the ground. Fourth & fifth pic, opens space where reso was and replacement tail pipe section where the resonator was:
The MDS system on your truck will introduce more drone than an non-MDS equipped engine will due to the soundwaves it produces in the system.
You can attenuate that by 1) don't go full auto or, 2) tune the truck and remove MDS.