That's closer to mountain gearing.. Or rather, that is a mountain bike rear cassette... So it will be easier to get up hills. they do that with"touring bikes" because you're likely to be carrying weight on the bike and you need some smaller gears to be able to deal with that.

People that live in very hilly or mountainous areas sometimes put a mountain bike rear cassette on a bike as well.

If you look you at your trek and you count the teeth of the largest cog in the back, that'll tell you what size cassette you have - you probably have something like an 11-25 cassette. So the smallest gear you can get into on the back is a 25 tooth cog. The largest cogs they make for road bikes is 27 or 28 teeth (depending shimano or sram... there is a company that makes bigger cogs for road bikes, but then you usually have to change your rear derailleur to a mountain bike one and it's a third party company)