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I get the idea of ratios and the obvious that a smaller gear on the front and a larger one on the back will give you an easier end result but what difference does the range of a chainset or groupset make?
I guess a related question is, Why do higher end bikes have only two sprockets on the front while lower end ones have three? (apart from any weight implication)
Its not about higher and lower end bikes, its about the nature of the bikes and the purposes they are used for and probably some history and snobbery too (-:
You can pay a truly staggering amount of money for a mountain bike (or a tourer or a recumbent) with a triple chainset and equally you can get something that bears a passing resemblance to a road racing bike with a double chainset for a relatively small amount of money (though its a bit harder than finding something cheap that resembles a mountain bike).
You can't ignore weight either - because the bikes with doubles on tend to be road racing bikes and for those weight is significant - as is complexity, removing a front ring (only having two) reduces the chances of you being in the wrong gear or having to make an overly complicated change at a critical moment - however it reduces the range of gears and, if you've watch pro cyclists struggling with genuinely steep hills (e.g. in the UK) you'll know that this can be an issue - although seldom in the Tour de France where the hills are long rather than particularly steep.
Look at city bikes and - assuming they use a derailleur - you'll sometimes see a single chainring at the front and again possibly on a bike that costs more than you might expect.
I've not answered the question so...
The gear range for a bike is substantially dictated by the lowest gear - you start with what you need to deal with the ascents you will be tackling (based on your personal abilities and other factors) and then cover a range dictated by your gearing 'til you get to a top gear. You hope that you end up with something that allows you to complete the climbs whilst not spinning out (getting to the point where you can't pedal fast enough) too early on the descents or whilst on the level. Ideally you'd like the ratios available between the two ends to be reasonably evenly spaced and easily selectable.
Mountain bikes tackle more extreme slopes so need lower gears - hence want triples. Touring bikes tackle the slopes with more weight, so need lower gears - hence want triples. On a recumbent you want to spin up hills in a low gear but are even more keen on being able to turn a high gear - hence want triples (and sometimes more to extend the gear range). On a "road" bike you're assumed to be fitter and stronger and to pedal with a higher cadence - you also want less weight so you give up on the extra chainring.
The answer to your main question is cadence, i.e. the rate at which you rotate the pedals. Most cyclists naturally tend towards a narrow range of cadences where we feel most comfortable. We also have different comfort levels / capabilities for power output.
To spin comfortably up a hill (at your preferred cadence and effort level) you'll need to find a gear that's low enough to match. For me, that's going to be a pretty small gear; for a pro racer (who can put out lots of power over long time periods) it would be substantially bigger. The same thing happens on a flat or downhill: if the gearing is too low you'll start to "spin out" (too high a cadence with not enough effort). Again a racer is likely to need a bigger gear to keep this from happening.
So that explains the overall gearing range. The steps between gears can matter too: if they're too big you may have trouble dialing in the perfect gear that matches your desired cadence and power output. On racing bikes you'll notice that despite having many gears, the overall range is still fairly small. The difference is that the step between each gear is more subtle. (My bike has a fairly wide gear range, so these steps can become quite noticeable as I get tired.)
As for your related question, Murph has nailed it: high end racing bikes tend towards two chainrings because of need, weight, complexity and fashion.
Primarily, the range of your drivetrain affects your fastest and slowest speeds (for a given cadence).
Often there is no perfect range and selection of gearing will normally involve some compromise (Either losing top end speed or making climbs difficult).
The importance of the gear range of your drivetrain therefore varies with your usage scenario, and snobbery (@Murph!).
More front chainrings = more range, higher weight, more maintenance.
Less front chainrings = less range, lower weight, less maintenance.
Here are the options:
Front Rings Total Gear Range
1 Smallest
2 Medium
3 Largest
4+ Now You're Just Being Silly
Total gear range is limited by chain and derailleur technology and mechanical limits. For example, it's obvious that if you have a very small to a very large cog in the cassette the chain will need to be long to accommodate the length difference as the chain goes around. The derailleur must also be able to physically move the distances involved and take up the slack in the chain. (This, incidentally, is why mountain bikes with their large range tend to have long cage derailleurs) There are limits with how different the cogs can be.
It is very difficult to judge the 'high-endianess' of a bike by the number of front sprockets. Some of the most expensive bikes I've seen have only one chainring, either for weight, maintenance or aesthetic reasons.
