Definition
Consumer's Risk is the probability of making a Type II Error - failing to reject the null hypothesis when it is, in fact, false. In hypothesis testing it is denoted by the Greek symbol ?.
Examples
If you think of the final inspection of a product in a factory, why this is called Consumer's risk becomes clearer. The null hypothesis for the inspection process is that the product is acceptable. If the product is found to be acceptable when it is actually defective, it will be sent to the consumer when it shouldn't have been. This causes the consumer to incur unnecessary costs because they will have to return the product or have it repaired.
Application
When you set the beta level for a hypothesis test, you are setting the level of consumer's risk you are willing to accept.
See Also
Type II Error
Power of a Test