To illustrate, I've taken the gear ratios from a couple of my household bikes and plugged them into Sheldon Brown's Gear Calculator. This is a fantastic tool that will tell you exactly how much work you're putting into getting from A to B. Things get a little more complicated when we factor in that both of these bikes feature derailleur gearing, rather than internal hub gearing. They are also about 10 lbs apart in weight, which will affect speeds both uphill and downhill (this becomes more extreme when we add the bodyweight of the rider). However, most Americans have bikes with derailleur gearing, so we'll make an assumption of all other things being equal for the sake of argument.
Here's the chart for my Surly Long Haul Trucker, which has 3 chainrings in the front, and 9 cogs on the cassette in the back for a total of 27 gears.
Here's the Trek FX 7.1, which is has 21 gears total (3 in the front, 7 in the back).
You can interpret these charts to mean my bike has both a higher and a lower gear range than the Trek, so it both goes faster on the downhills and gets up hills a little easier, assuming a cadence of 80 revolutions per minute. It also has more gears, so there are smaller jumps between the gears, which is mechanically speaking easier on the moving parts of the drivetrain.
What becomes obvious though is how similar the upper and lower ranges of the two bikes are, despite the fact their drivetrains are in other ways significantly different. This information is the easiest way to understand out what you're getting into with gearing, and for me at least, visually explains the real-world connotations of the gear range of a potential bike.