Jumbo acoustic guitars have a few advantages when compared to dreadnought-style acoustic guitars. At a glance you can see they have larger bodies, meaning a bigger sound chamber and soundboard. This means:
Better projection: Because they are bigger, jumbo guitars tend to project better, especially for the mid-range and bass frequencies.
Better volume: This is a great advantage if you are playing with a group, especially if you do not have sound reinforcement.
Better bass response: Jumbo-bodied guitars have great low-end, so your bass strings will ring loud and clear.
Better sustain: Notes ring longer, and chords chime with excellent resonance.
Great for strumming: All of the points the above means a jumbo acoustic guitar is a smart choice for flat-pickers and guitarists who mostly strum. While not the best choice for playing finger-style, they are passable, especially if you choose an acoustic-electric model with a flexible EQ in the preamp.
Country and rock players tend to gravitate to larger, jumbo-style guitars because of all the traits listed above. These guitars are loud and bold enough to use in a band, and can stand out in the mix. They also look really good onstage, in my opinion.
With all of that loud, bassy strumming goodness comes a few downsides. Because of their large bodies, jumbo acoustics can be tough to manage for smaller players. Many instead go with a dreadnought, a guitar style that still has very good volume and projection but is a bit smaller.
However, don’t let size dissuade you if you think you want a jumbo. There are many diminutive players who do just fine with larger guitars, after a little practice.