The Letter X indicates the Roman numeral for ten, and the Latin term "Decem." This represents a 1:10 dilution factor. It can also be labelled as DH or D for "decem;" therefore, X is the same as DH or D.
The Letter C indicates the Roman numeral for one-hundred, and the Latin term "Centum" to represent dilution stages made in the 1:100 ratio. The C dilutions are often labelled as CH. This is equivalent notation, since the H is superfluous and often dropped in C-type or D-type preparations.
The "H" in "CH" or "DH" simply indicates that the process is by Hahnemann's method. This is often dropped because it is assumed that the process is Hahnemenn's. Occasionally, a "K" is indicated to communicate that the process was by the Korsakovian (K) method instead of the usual Hahnemannian (H) process. When only C, D or X is stated, the H is assumed. If the process was by Korsokov's method, there will always be a K to indicate this.
What do the numbers mean?
The number indicates how many times the dilution process was repeated, and it gives us a sense of how diluted the labelled substance is. The previous dilution stage is used to produce the following stage. This is done in serial sequence, amplifying the dilution, and is known as "serial dilution" or "series dilution." For example, a 2X dilution is prepared from a 1X preparation, and a 7CH dilution is prepared from a 6CH preparation; therefore, each step exponentially dilutes the original substance, with the number indicating how many times this process was repeated. It is universally accepted that it is possible to dilute a substance out of a sample. This occurs providing that the original substance is not bound to the vessel, or otherwise partitioned from the diluent, and that the diluent stages sufficiently mix to homogeneity with each dilution step. If dilution is complete and homogeneous, then the original substance will be diluted away from the preparation after approximately 12 cycles or less.
In a X factor preparation the 12X is approximately a 1:1,000,000,000,000 parts mixture and in a C factor preparation, the 12C is approximately 1:1,000,000,000,000,000,000,000,000 parts substance to diluent. Therefore, a 200C is diluted 100 to the power of 200, which is 1 with 400 zeros. By comparison, there is approximately 1 ( with 24 zeros ) litres of water on the earth (according to HowStuffWorks contributors). The number of zeros can be determined by the dilution number for an X type, or twice the number for a C type since base 100 = 10x10, (10 to the power of 2).
Since the excess of each stage is removed, and only 1 part remains to form the following stage, each dilution step is accomplished with minimal waste, and the remaining qty is saved to form other preparations later. In other words, 10mL of a mother tincture are used to prepare a 1C dilution by adding 990mL of water. Then shaken. 10mL of the 1C dilution are used to prepare a 2C dilution, by adding 990mL of water to a new vessel, and so on the process is repeated 200 times to create the 200C dilution.
For more information search for articles on "Avagadro's Number" and "Serial Dilution"
This is to clarify that the numbers and letters do not indicate dose, but instead indicate the preparation's factor of dilution. In homeopathy, the dose is measured by the number of pellets, tablets or drops consumed of that preparation. The amount of the labelled substance in the pellet is not viewed as important in homeopathy, only that the dilution process began with that substance.