Why can electricity flow only in one direction through a diode? A few days ago I was soldering a small thing which contained a diode, a battery and some other useless things.
Unfortunately, I soldered the diode reversed and it didn't work. When I reversed it again it started to light.
I was trying to find an answer in Google, but the only thing I could find was the fact that electricity in diode can flow only in one direction, but my question is why? How does it work? Is this fact connected with the construction of a diode?
 A: Let me try yet one more type of explanation, which I will confine to the PN junction diode (covers virtually all diodes used in modern circuits).
The diode consists of a p-doped region (p-type) slapped up against an n-doped region (n-type).  In the p-type, the electron (e-) flow is largely accomplished by electrons moving from hole to hole. This is, electrically, exactly analogous (and is often visualized) as holes moving in a direction opposite to e- flow (although there is no physical movement of postivie charge)  In the n-type, there are loosely bound e- which can be donated (moved).
At the PN junction of the diode, loosely bound e- in the n-type fall into the holes of the adjacent p-type.  What you then have is an abundance of e- in a thin layer of the p-type layer at the junction, and a depletion of them (creating a net positive charge) in a thin layer of the n-type.  This sets up a voltage field of positive in the n-type relative to negative in the p-type.  This pushes any free e- in the n-type further away from the junction.  The result is a thin PN layer which has no free holes and no free e-.  The layer becomes an insulator.
Now, if you apply a positive voltage to the p-type and a negative at the n-type, e- in the p-type are removed, making free holes.  Simultaneously, the positive voltage is conteracting the reverse voltage which had been set up in the PN junction, and e- in the n-type are force closer to the p-type, where they can cross over and fill up the new holes.  Current flows.
If, however, you apply positive voltage to the n-type, and negative to the p-type ("reverse-biasing" the diode) you simply reinforce the voltage gradient which was already naturally set up in the PN junction.  The e- are forced even farther away from the PN junction, and the insulative boundary (depletion region) thickens.  No current flows.
To get more in-depth than that might take a good portion of a graduate course in materials science.  I hope what I have written suffices.
A: A diode consists of two materials known as p-type and n-type semiconductors, connected in series which allows current to flow through them differently. In the n-type semiconductor, electrons travel with enough energy such that they're not attached to an atom and are said to be in the conduction energy band. For the p-type semiconductor, electrons "hop" from atom to atom, but lacking the energy to free them, are said to be in the valency energy band.
At the interface between the n-type and p-type materials, a travelling electron has to move either from the n-type to the p-type in one direction, the p-type to the n-type in the other, to continue moving. Is there a difference between the two directions?
Well, an electron moving from the n-type to the p-type material can occur spontaneously because the free electron's energy is released as radiation and it can move to a lower energy state, attached to an atom in the p-type semiconductor. But to move from the p-type to the n-type it has to gain energy from somewhere, and this isn't spontaneous because there is no guarantee of some other process providing this energy.
Think of a ball at the top of a hill: It can move from the top to the bottom while spontaneously releasing energy, but some other process must provide the energy to take it from the bottom to the top. And this analogy provides a basic explanation for why a diode conducts in one direction, but not in the other.
A: This really depends on the type of diode you are talking about but for the most common types there is something called a PN-Junction that allows current to flow in only one direction.  This page:
http://en.wikipedia.org/wiki/PN_junction
on wikipedia explains how a PN-junction works.  The short version is the voltage has to be above a certain threshold defined by the materials in the junction before the juice can flow.  This shows up in the I-V characteristic curve as a point in the plot where the derivative is discontinuous.  The details on other features of the I-V curve are up for grabs depending on the materials used but it's the junction and the application of a voltage beyond that threshold that means you have a diode on your hands.
