An Acoutic Model is a file that contains statistical representations of each distinct sound that makes up a spoken word (called phonemes).  It must contain the sounds for each word used in your grammar (or language model).

An Acoutic Model is one of the components that make up a  Speech Recognition Engine ("SRE").  Also included in an SRE are the following:

• Language Model for dictation, or Grammar for IVR or desktop Command and Control applications, and a
• Speech Decoder - the actual speech recognition software. 

The decoder takes the sounds spoken by a user and searches the Acoustic Model for the equivalent sounds.  When a match is made, the decoder determines the phoneme corresponding to the sound.  It keeps track of the matching phonemes until it reaches a pause in the users speech.  It then searches the Language Model or Grammar file for the equivalent series of phonemes.  If a match is made it returns the text of the corresponding word or phrase to the calling program.