Overview
A generic definition of an incomplete market is a market in which there are more sources of randomness than there are traded assets. Generally, this means that there are sources of randomness that are not traded.
For example, the temperature in Chicago is a measurable process, but it is not traded. If one wanted to create a derivative that was derived from the temperature in Chicago, you would not be able to create a replicating portfolio by trading the underlying. (the temperature in Chicago)