My interpretation: A short, light, quick-handling, hard-hitting rifle which shoots large, heavy hunks of lead that'll be less affected by brush (ie: bushes, twigs, sticks, branches, etc.).
I'd consider rifles or carbines chambered in .44Mag, .30-30, .45/70 and the like to be "brush guns."
For example, a Marlin Guide Gun chambered in .45/70 would probably be more at home in the brush than a Remington 700 chambered in .222. The .45/70 bullet will go through most obstacles that would likely shatter, fragment, or deflect a .222 bullet.