The Dragon is designed to be able to bring unpressurized cargo to the ISS. How can such cargo be brought on board the ISS? What uses can such unpressurized cargo have?
Unpressurized volume is used to deliver payloads that will be used externally on the International Space Station (ISS), i.e. external cargo. It also holds the two Dragon's solar panels and about 14 cubic meters is available for other unpressurized cargo, or 34 cubic meters with extended trunk.
One such example unpressurized cargo was the RapidScat that was delivered to the station aboard the Dragon SpX-4 and installed on Columbus module's External Payloads Facility (CEPF) by Dextre (Special Purpose Dexterous Manipulator) on Canadarm2. Here's RapidScat in action as seen from one of ISS external cams:
The whole installation of RapidScat, along with some additional info on Dragon's unpressurized volume, are described in detail in Dragon SpX-4 Mission Updates Spacefligh101 article. Same source also has an extensive article on the RapidScat. Wikipedia on Dragon spacecraft adds that the first Dragon to deliver unpressurized cargo to the ISS was the SpaceX CRS-2 mission that delivered two Heat Rejection Subsystem Grapple Fixtures (HRSGFs).
NASASpaceFlight elegantly and concisely describes this Dragon's capability with:
CRS-2 will debut the use of Dragon’s Trunk section, capable of delivering unpressurized cargo, prior to the payload being removed by the ISS’ robotic assets after berthing.
Only other cargo delivery vehicle to the ISS that is currently also capable of delivering unpressurized cargo is JAXA's H-II Transfer Vehicle (HTV) with unpressurized payload mass of 1,500 kg.
There are many payloads that are large, and need transport to the station. Things the Shuttle used to provide.
If you carried them pressurized, they would need to be sized to fit through the CBM port to get out of the Dragon, then through one of the airlocks (Quest or Russian side) to get out of the station.
The Shuttle left some large line replaceable units (LRU) on the truss as spares. Should that supply be exhausted, Dragon could launch more.
The CanadaArm can reach in and grab the payloads and move them as needed.
I think you're looking at it backwards. It's not "how is unpressurised cargo useful?"; it's "how is pressurising cargo, that doesn't need to be pressurised, useful?" It's "what can I ship up to the ISS that doesn't need to be kept at atmospheric pressure the whole time, with all the space and logistical requirements that this adds?"
Anything that doesn't need to be squeezed into the station's habitable area can simply be kept unpressurised during launch, and removed from the supply ship externally using the CanadaArm, which is great!
This is pretty much reduced to technology that will live outside of the station long-term, since you'd otherwise have to cram it into an airlock anyway in order to get it inside.
As an analogy, suppose you are taking an airplane flight from New York to Los Angeles. Knowing in advance that the airplane food, if any, will be garbage (said nicely), you buy some food to take with you on the flight. When you partake a couple of hours into the flight you notice that your bag of potato chips seems to be about to explode, but your nice sandwich remains about the same as you bought it at sea level.
Both your sandwich and your bag of potato chips are in this sense "unpressurized cargo" (but see below). With regard to your sandwich, it's still edible because the approximately 1/3 drop in pressure isn't near enough to make it inedible. With regard to your bag of chips, it's still edible because the bag was sealed.
Getting back to the problem at hand, anything that can handle the drop from one atmosphere of pressure to vacuum is "unpressurized cargo." Some items are sealed against vacuum, so it's fine to expose those items to vacuum. Other items are oblivious to pressure changes, so once again it's fine to expose those items to vacuum.
Stuff that can't handle anything close to that drop in pressure from one atmosphere to zero is "pressurized cargo." This stuff needs special handling.
For example, the passengers in a modern airliner need special handling. The pressure in the cabin of such an airplane is not ambient. The pressure inside an airplane that flies from New York to Los Angeles is instead an artificially maintained environment. The pressure at the altitude at which that airplane flies is extremely low. If exposed to that low pressure, you would die in short order. Even peoples who have had generations of acclimation would die if exposed to that pressure. The passenger section of a modern airliner is a pressurized cargo space.