Modem's modulation

In order to send or receive data, the modem has to encode/decode the information in a way that it can be transferred over the physical line. This encoding/decoding is done using  symbols.
The modem holds a 'map' of symbols (a symbol stands for a different length "word" of bits, which two modems agree upon), and the symbols are transmitted over the physical line. Each symbol represents 1 bit of data or more.
For example, if a modem uses four symbols, each represents two bits (00, 01, 10, 11). Eight symbol spaces can represent three bits each, etc…

When transmitting a symbol, a random noise (Electrical, magnetic, influence of the environment or other transmissions) might be added to the symbol. The symbol will then be moved from its original location in the symbol space. The receiver then needs to decide what symbol was transmitted. It might compare the received signal to the symbols map and choose the nearest one. It is needless to say that this decision may be wrong.

When noise level is increasing or when the symbols map is crowded, higher error rates will result. We cannot stand high error rate, hence in a given noisy environment, the symbols map cannot be too crowded.

The following slideshow shows an example of modulation.