What is homogeneous/heterogeneous equilibrium?

First, let's break down the words so it will be easier to
remember.  Equilibrium means that things are in a state of balance.  Homo is a Greek
prefix that means same, and hetero is a Greek prefix that means different.  A
homogeneous equilibrium is where everything in the reaction reaching a balance is in the
same phase.  An example would be when everything in the reaction is in the gaseous
phase.  A heterogeneous equilibrium is where the reaction is balanced but the agents of
that reaction are in different phases.  An example would be a reaction between a gas and
a solid.  See the links below for more details.  The chemguide link also contains
equation examples in case you need them.