An Acoustic Model is a file used by a Speech Recognition Engine for
Speech Recognition. It contains a statistical representation of
the distinct sounds that make up each word in the Language Model or
Grammar. More information can be found on the Background re: Acoustic Model Creation Document.
A Speaker Dependent Acoustic Model is exactly what its name suggests - it is an Acoustic Model that has been tailored to recognize a particular person's speech. Such Acoustic Models are usually trained using audio from a particular person's speech. However you can also take a generic Acoustic Model and adapt it to a particular person's speech to create a Speaker Dependent Acoustic Model.
A Speaker Independent Acoustic Model can recognize speech from a person who did not submit any speech audio that was used in the creation of the Acoustic Model.
The reason for the distinction is that it takes much more speech audio training data to create a Speaker Independent Acoustic Model than a Speaker Dependent Acoustic Model.