Why can one bend glass fiber? Why can one bend glass fibers without breaking it, whereas glasses one comes across in real life is usually solid?
Is there also a good high-school level explanation of this?
 A: The critical parameter for materials under stress is the strain, defined in a general way{*} as the fraction change some length over that same length:
$$ \lambda = \frac{\Delta l}{l} $$
So take a given a fiber of diameter $d$, and bent around a radius of curvature $r$, the strain of either the inside or outside edge is:
$$ \lambda = \frac{((r \pm d) - r) \theta}{r \theta} = \pm \frac{d}{r} $$
Now you need only look up the breaking strain for the glass in question.

{*} Or fractional change in volume over volume, or displacement as a fraction of length, or... It really depends on the details of the situation you're trying to measure, but the above definition will work for tension and compression.
A: Having spent a great deal of time working with "normal" glass (one of my many hobbies), I can assure you that, in fact, all glasses can be bent. When cutting large sheets of glass, I always see the sheet bend before it breaks. Every now and then you have to strike it twice; the first time you bend it, it fails to break. Fiber optics differ from the usual glass partly in that it is very thin and so bends much more easily. After you've cut a few thousand pieces of glass you come to recognize differences between different compositions. Some glasses feel very smooth when they bend, others, like the stained art glass shown below, are rather ragged and difficult to bend. (And all breaks or cuts in glass begin with a bend.)
To get a more familiar metaphor, think about wood. It doesn't surprise you when a slat of wood that is 1mm in thickness is bent in a circle. Now imagine doing the same thing with a much thicker piece of wood. You can't do it with the thicker wood because it's too thick.
In addition, regular glass differs from fiber optic glass in that fiber optic glass is very pure and this makes it very strong. In the art glass community, thin glass rods is called "stringer". Let me see if I can find some photos of cold stringer being bent.

Okay, I found some clear stringer. I put it on a sheet of stained glass supported by two pennies. I took two photos, before and after pressing the stringer in the middle. You can see the bending. Straight:

Bent:
 
A: In addition to the question of bend radius - there is also an effect of surface scratches.
Most materials are very strong - they fail because a surface flaw allows a stress concentration - ie a crack to form. glass fibre has a very smooth surface because of the way it is made and can be put under high stress without cracking.
You can show this with a thick glass rod (or you could before we were banned from doing anything interesting by 'safety'). Clean the surface with acid, or heating and annealing,  so any defects are removed  you can then bend the rod like rubber. But touch the bent part with a metal ruler to create scratches and it will shatter
A: See the difference between optical fibre and a normal glass, comprises of two things.
First one its too thin having a dia. of 125 micron and the other thing is the coating which is used to increase the strength of fibre and make it bend resistant.But there is a also a limit upto which you can bend the fibre and crossing that limit will result in breaking of the fibre.
A: Anyone ever see video of a normal drinking glass being targeted by soundwaves at very slow speed? If so, then you will know already how flexible even dirty glass is. In the video, as the sound gets closer to the harmonic resonate frequency of the glass, it warps the glass ever further. Once the resonate frequency is matched, the glass breaks.
Fiber is just a whole lot thinner, also a whole lot cleaner and pure than drinking glasses are. This two combination of size and purity equals flexibility and strength, allowing the fiber to be put through all kinds of torture before reaching the failure point.
When I was a fiber optic technician/installer, the was amazed at how thin and flexible the fiber was. In outside plant, we had fiber lines in bundles, without the benefit of the shielding you see in patch cords. The fiber was basically bare, only a  color coded cladding was inside the cable, similar to the color codes of copper wires (blue orange green brown), we installed the "break out" kit, giving each fiber a sheath before having to polish the fiber ends using micron sand paper and a scope.
Either way, I put fiber optic cable in my "magic file" of things that defy logic. 
