Cassette/Freewheel/crank
 

I don't understand this 12-26t, 11-32t?
48/38/28?

What does it stand for?

12-26 or 11-32. The numbers refer to the number of teeth on the rear gears. Only shows the biggest (lowest) and smallest (highest) cogs.
48-38-28. The chainring sizes on the crankset (front gears) are 48 (highest), 38 and 28 (lowest). Again shows how many teeth are on each ring.

So then what is the difference in the sizes of them and how does it benefit me?
Plus how do I know which size to get or does it matter much?

Here is a wiki article on bicycle gearing:
http://en.wikipedia.org/wiki/Bicycle_gearing
And another from Livestrong:
http://www.livestrong.com/article/25...ng-bike-gears/

Here's a calculator that allows you to calculate the gear ratios. Here's another that more visual.Here's one that allows you to see it a bit more graphically.

So does it means that the more teeth the less it takes to pedal to make the wheel turn and the less teeth the more it takes to pedal to make the wheel turn?

Depends on where the teeth are. If you have a large number of teeth at the crankset and a small number of teeth at the wheel...the 48/11 combination...it takes fewer revolutions of the front crank to move the rear wheel further. For the 48/11 combination, for a single spin of the front crank, you are moving the bike 9.8 meters down the road. If you go to a 48/32 combination, you are moving the bike 3.2m down the road. On the other hand, if you use the small ring in the front and the large cog at the wheel...the 28/32 combination...you move the bike 1.9m down the road.

It's probably easiest to remember as big front/little back, you go fast. With a little front/big back combination, you go slow.

Gearing is a ratio. Front divided by rear, times wheel diameter. More teeth in front makes the number bigger, more teeth in back makes the number smaller.

As for cassette ratios, the small numbers and large numbers are important. The smaller the small number, will give you a higher maximum gear. The larger the larger number will give you a smaller minimum gear. So why not go for the biggest spread like an 11-32? Well, that causes bigger gaps between gears. When you are riding, making small changes to your gearing is a big help. That is why gearing like 12-23 is popular.

On the chain rings like 53-39 a similar thing is happening. The bigger the big number, the larger you maximum gear. The smaller the small number, the smaller your minimum gear. A triple chain ring gives you a bigger range with a slight degradation of shifting "crispness". Also triple chain rings are viewed by many road riders as not stylish. Mountain bikes on the other hand, seem to always be triples.

To add to PatW's explanation, some derailleurs (both front and back) are designed to work only with certain cassette and chainring sizes; many road bike rear derailleurs have a maximum cog size--can't take larger than a 28/30. This becomes more pronounced the more high end/specialized the derailleur gets.
Front derailleurs are a bit more complicated. Not only are the cages slightly different shapes depending on if it is intended to be used with double/triple configurations (53/39 vs 52/42/30) AND are shaped according to the largest size (i.e. diameter) ring they are intended for (46 for a mountain bike derailleur, up to 55 for a road bike FD), they also have a chainline issue. The chainline is the number that describes how far from the centerline of the frame the chain runs; in externally-geared bikes, it describes the middle of the FD's movement. This number is different for road bike and mountain bike derailleurs since mountain bike cranksets ride further out from the bottom bracket in order to clear the chainstays/tires when using smaller gears. If you use a road bike front derailleur on a mountain/touring (73mm) bike frame with a mountain triple, your FD can't swing out far enough to shift onto the big ring. This is typically only an issue with touring/cyclocross bikes and homemade 2x MTB's, but can come up when looking for replacement parts.

Okay so a 12-26 would be a lot better than having a 11-32, because it doesn't have a such a big gap in between the smallest to the largest?

So if that's the case, then I have nail down to two bikes. What do you guys think? I know it's not the best, but it's in my budget.

http://penncycle.com/product/11trek-...on-72264-1.htm
http://www.bikesdirect.com/products/...alaxy_tour.htm

Ride up the steepest hill you have. If you can make it 'easily', you don't need to change a thing. Basically that is what it comes down to. The rest you should be able to figure out by what happens when you shift to different cogs. And if you don't have a bike and don't know what it means, then ride one, shift it and it all will make sense (or should). That is the easiest way to explain it without going into detail to where the explanation is so complicated it doesn't make sense. It really is an extremely easy concept.