The chromatic semitone is the difference between two adjacent notes on the chromatic scale and is thus approximately one twelfth of an octave.
For example, the difference between C and C# is one chromatic semitone.
The term "semitone" usually makes sense only when discussing notes on the chromatic scale and scales that use notes from the chromatic scale, such as common heptatonic scales as the major scale or the natural minor scale. Thus, "semitone" usually means specifically the "chromatic semitone".
The chromatic scale is a scale of 12 semitones covering one octave. One octave (for example, A = 440 Hz to A = 880 Hz) is bound by two frequencies the ratio between which is 2 (880 / 440 = 2). One semitone should be approximately the ratio of 2^{1/12}. If the twelve semitones on the chromatic scale are equal then the chromatic scale is equal tempered and each semitone is exactly 2^{1/12}. In other words, the ratio of the frequencies of C and C# in the same octave is C# / C = 2^{1/12}. Similarly, D / Db = 2^{1/12} and so on. If the chromatic scale is not equal tempered, such as if it is a just tempered scale, then the semitones are not equal to each other and are only approximately, and not precisely, equal to 2^{1/12}.
See also:
Scale, Scale (index)