Those documentaries probably explain it better than I could! But I’ll give it a shot anyway.
A string, or superstring, is an entirely hypothetical strand of energy and the fundamental building block of the Universe. Superstrings are thought to be incredibly small - around 10^-33cm. That’s so small that if a superstring was the size of the Earth, a proton would be the size of the entire observable Universe.
Superstrings, if they exist, are thought to form the fundamental particles of matter (quarks, electrons, neutrinos and so on). The idea is that superstrings vibrate, like the strings on a guitar or violin. In the same way that one particular mode of vibration of a guitar string produces a C note, another produces a D note, another produces an F# and so on, the idea is that one mode of vibration of a superstring produces an electron, one produces a photon, one produces an up quark and so on.
Think about that. That means that all the properties of a fundamental particle: its mass, its stability, its electric charge, its weak charge, its colour charge and so on - are all just different ways for a superstring to vibrate. Theoretical physicists have duly set to work calculating how many ways a superstring needs to vibrate to explain all our particles, and it turns out there’s a catch.
A plucked guitar string will vibrate up and down, in two dimensions, producing standing waves like this:
It’s also possible to have standing waves in three dimensions. For example, whenever an earthquake takes place, vibrations pass through the spherical Earth, vibrating up and down, left and right, and back and forth. Standing waves set up here are a lot more complex and diverse than the kind of waves you can get on a guitar string. And for a superstring to be able to vibrate in just the right way, so that its allowed modes of vibration can explain all our familiar particles? That would require ten dimensions of space. Which means, when you count time as the fourth dimension, our Universe would not be three-dimensional but eleven dimensional. (Older versions of superstring theory say ten or 26, but 11 is the number of dimensions in M-theory, the latest version of superstring theory).
If the Universe is 11-dimensional, why do we only see three of space and one of time? One answer could be that the remaining seven dimensions are “too small to see.” You can understand this by thinking about a hosepipe. Close up, you can see it’s a 3D shape, but if you step back far enough, it just looks like a one-dimensional line. In that view, space looks three-dimensional to us, and all our experiments down to the particle scale show nothing more than three dimensions, but if you could somehow look really, really closely and zoom in to an extremely tiny scale, you would see space actually contains more dimensions than our minds could imagine.
So why would physicists think such a bizzare thing? Why would you assume all particles are actually vibrating strings in eleven dimensions? The answer is that superstring theory actually explains an awful lot. Physicists have two big theories - quantum mechanics explains the world on a subatomic scale and all forces except gravity can be worked into quantum mechanics. General relativity explains the Universe on a huge scale, the nature of space and time, and explains gravity. The two theories are actually mutually incompatible. Normally that’s not a problem, because gravity is so weak compared to the other forces that it doesn’t even show up when we’re considering atoms or subatomic particles, and so we don’t need to use general relativity and quantum mechanics in the same situation, and both theories work perfectly well in their own domains. However, physicists know the Universe can’t be inconsistent, so one or both theories must be wrong (or at least incomplete). And nowadays they’re starting to run into problems where particles are so close together and densities are so high that gravity becomes important on a quantum scale: the Big Bang, black holes, etc.
Superstring theory not only reduces all the dozens of known particles down to different vibrations of the same, one fundamental unit - it also helps to merge quantum mechanics and general relativity together into a bigger, all-encompassing theory that says “well, you’re both sort of right.” In quantum mechanics, forces are carried by force-carrying particles, but in general relativity, gravity is explained as curved space-time. Physicists have therefore assumed that a quantum theory of gravity would involve force-carrying particles, which they call gravitons, that would cause space-time to curve in the way predicted by general relativity, and have calculated the properties gravitons ought to have. And guess what? One of the allowed modes of vibration that superstrings have matches the predicted graviton exactly! Physicists weren’t even trying for a quantum theory of gravity when they came up with superstrings, but it turns out that string theory is one anyway! So superstring theory explains all known forces of nature (including gravity), all known particles and their properties, reduces everything in the known Universe down to just one basic unit (the superstring), and successfully combines quantum mechanics and general relativity, even in situations like the Big Bang and black holes where they wouldn’t previously talk to one another. No wonder physicists like it!
The problem is that at the moment there is absolutely no evidence for superstrings whatsoever. Many physicists have been working on alternative “Theories of Everything” to unify all the fundamental forces, or on alternative theories of quantum gravity. None have yet been as successful as superstring theory, but maybe one day, someone will come up with something better. Fortunately, string theorists do make a few predictions. One is the extra dimensions mentioned earlier, and physicists are currently working on ways to test that. Critics point out however that extra dimensions wouldn’t necessarily imply string theory is correct (although if we could somehow show that there were exactly eleven dimensions that would be a strong hint!)
Another prediction of string theory - at least, the modern version of it - is something called supersymmetry (that’s why current string theory is called “superstring theory” - a mixture of the original string theory and supersymmetry). Some of the allowed vibrations of strings are particles that would be very similar to the particles we’re familiar with but would be much heavier and wouldn’t interact much with ordinary matter. (For example, a “selectron” is a supersymmetric particle similar to an electron but a lot more massive and doesn’t interact as much; a “neutralino” is a supersymmetric particle similar to a neutrino but a lot more massive and doesn’t even interact as much as neutrinos do and was presumably named by Ned Flanders, etc.) Because supersymmetric particles are so massive, they’re hard to produce in particle accelerators (they’d need a lot of energy to be produced), and because they’re so weakly interacting, they’re hard to detect otherwise. Astronomers have figured out that most of the matter in the Universe is in the form of “dark matter,” an invisible, weakly interacting substance - so supersymmetry might explain that.
The problem with this is that the Large Hadron Collider hasn’t yet found any supersymmetric particles and by now it’s been colliding with energies high enough to be able to produce some. So some physicists are abandoning supersymmetry (and with it, superstring theory). Others say that perhaps supersymmetric particles have a much smaller range of masses than we thought, a range that the LHC hasn’t explored yet.
So string theory has a lot going for it but it suffers from a lack of evidence - for gravitons, for extra dimensions or for supersymmetric particles. Still, it explains so much that many physicists are hopeful that it’ll turn out to have a lot of truth in it.
I hope that helped, and if you’re still confused try http://www.superstringtheory.com/ or http://www.sukidog.com/jpierre/strings/, which are written by physicists and can explain it a lot better than I can!
Physicists reading this - if I’ve made a mistake, please correct me! I’m sure this is very very oversimplified because I can’t claim to understand superstring theory well myself, so I’m sure a few mistakes have crept in here somewhere.