There are two basic categories of fiber: Single mode and multi-mode. The "mode" refers to how the light is propagated through the medium (usually glass).
Multi-mode relies on the "critical angle" of light ... if the light strikes a surface at a shallow enough angle, it is reflected, so transmission through multi-mode looks like "/\/\/\/\/\/\/\/\/\/." Since propagation is reliant on bouncing / reflection, the light source is generally something like an LED, usually at 650 or 850 nanometers (nm).
As mentioned above, the most common glass core sizes (for multi-mode) are 50 and 62.5 nm. To aid the internal reflective properties, a "cladding" is applied to the glass, which expands the diameter of the fiber, usually to 125 microns. The fiber diameter is usually expressed as glass core / cladding ... so standard MM fiber is usually 62.5/125 or 50/125.
Single mode fiber is much thinner (8.3 - 9 micron). Transmission is what the names says: single mode, i.e., a single straight line (no significant internal reflection) - "straight line" meaning follwing the path of the glass ... coaxial to the outside diameter .... like "--------------." The light source for SM fiber is usually some flavor of LASER / LASER diode (coherent, monochromatic light). Single mode also has cladding, usually out to 125 micron (8.3 / 125).
For either of the above, there are a bunch of "flavors." The glass comprising the fiber core is (usually) not a single consistant density. The center of the core is less dense, the outside of the core is more dense - the variable density ("stepped index" is one example) aids in reducing loss / increasing the reflective or conductive properties of the core boundries. There are a large variety of fiber types within each category ... each type is suitable for specific applications.
The glass core is so thin (in either type) and supported by coatings and insulators that it's amazingly flexible. You can tie it in a knot (not a tight knot, but a knot). Minimum bend radius for jumper-style fiber is ~1-2 inches in diameter. The downside to sharp bending is that it increases loss (in either type, but more in MMF).
The type of fiber used for the "Fiber-to-the-Premises" (FTTP) is almost certainly single mode (to accommodate the distances). It will terminate in a little box on the outside of the building, similar to a telephone "NID," and from there the individual signals will be distributed on traditional copper media.
The only exception to any of the above is the fiber used in Audio / Video (TosLink). It's a plastic fiber, somewhere around 500 micron. As fiber goes, it's total crap ... but more than sufficient for the purpose.
Also note that different applications use different frequencies (colors) of light. The A/V and 10Meg Ethernet (and other non-networking applications) use 650nm - visible Red. 100Meg Ethernet, Gig Ethernet, and other applications can use 850 nm (not visible), 1380nm (not visible), 1550nm (not visible). The point here is safety: NEVER LOOK AT A POTENTIALLY EMITTING SOURCE ... IT **WILL ** BURN THE RETINA AND PERMENANTLY DAMAGE YOUR EYES!!
That means: don't look at one end of a fiber unless you can see that the other end is not plugged into anything. Never look into a fiber optic recepticle / jack / outlet. There are "LASER goggles" available to wear if you work around an environment where LASER emitters are frequently active.
As is frequently the case, there are volumes of specific technological details for all of the above ... so the standard disclaimer applies: Some information may have been bent, folded, spindled, or mutilated for the sake of clarity and brevity.
FWIW
Scott