The component at the heart of most amplifiers is the transistor. The main elements in a transistor are semiconductors, materials with varying ability to conduct electric current. Typically, a semiconductor is made of a poor conductor, such as silicon, that has had impurities (atoms of another material) added to it. The process of adding impurities is called doping.
In pure silicon, all of the silicon atoms bond perfectly to their neighbors, leaving no free electrons to conduct electric current. In doped silicon, additional atoms change the balance, either adding free electrons or creating holes where electrons can go. Electrical charge moves when electrons move from hole to hole, so either one of these additions will make the material more conductive. (See How Semiconductors Work for a full explanation.)
N-type semiconductors are characterized by extra electrons (which have a negative charge). P-type semiconductors have an abundance of extra holes (which have a positive charge).
Let's look at an amplifier built around a basic bipolar-junction transistor. This sort of transistor consists of three semiconductor layers -- in this case, a p-type semiconductor sandwiched between two n-type semiconductors. This structure is best represented as a bar, as shown in the diagram below (the actual design of modern transistors is a little different).
The first n-type layer is called the emitter, the p-type layer is called the base and the second n-type layer is called the collector. The output circuit (the circuit that drives the speaker) is connected to electrodes at the transistor's emitter and collector. The input circuit connects to the emitter and the base.
The free electrons in the n-type layers naturally want to fill the holes in the p-type layer. There are many more free electrons than holes, so the holes fill up very quickly. This creates depletion zones at the boundaries between n-type material and p-type material. In a depletion zone, the semiconductor material is returned to its original insulating state -- all the holes are filled, so there are no free electrons or empty spaces for electrons, and charge can't flow. When the depletion zones are thick, very little charge can move from the emitter to the collector, even though there is a strong voltage difference between the two electrodes.
In the next section, we'll see what can be done to change this situation.