Monophone: The pronunciation of a
word can be given as a series symbols that correspond to the individual
units of sound that make up a word. These are called 'phonemes'
or 'phones'. A monophone refers to a single phone.
Triphone: A triphone is simply a group of 3 phones in the form "L-X+R" - where the "L" phone (i.e. the left-hand phone) precedes "X" phone and the "R" phone (i.e. the right-hand phone) follows it.
Below is an example of the conversion of a monophone declaration of the word "TRANSLATE" to a triphone declaration (the first line shows the "monophone" declaration, and the second line shows the "triphone" declaration):
TRANSLATE [TRANSLATE] t r @ n s l e t
In the CMU dictionnary, which has close to 130,000 word pronunciations, there are only 43 phones, but there are close to 6000 triphones.