According to my Wiley book, production and use methods are depreciation methods based on activity instead of useful life like the other more common methods (straight line, declining balance, etc.)

Activity (or use) would be machine hours. Ouput (or production) would be finished widgets.

Example:

Machine costs $60,000. Output is expected to be 500,000 units total. If the machine's output the first year is 100,000 units, the depreciation taken would be $12,000.

Depr  =      Current activity or output      x     Depr base

             Total expected activity/output

Depr  =  100,000/500,000  x  60,000  =  $12,000

Hope that answers your question.