What is "enzymatic activity"?
An Introduction to Enzymes (pdf) can be found here.


  Excerpted from a very popular Worthington publication which was
  originally published in 1972 as the Manual of Clinical Enzyme Measurements. While some of the presentation may seem somewhat dated, the basic concepts are still helpful for researchers who must use enzymes but who have little background in enzymology.


Source: Worthington Biochemical Corporation.

The quantity or concentration of an enzyme can be expressed in terms of activity in enzyme units. See Wikipedia:


  Enzyme activity = moles of substrate converted per unit time = rate × reaction volume. Enzyme activity is a measure of the quantity of active enzyme present and is thus dependent on conditions, which should be specified. The SI unit is the katal, 1 katal = 1 mol s−1, but this is an excessively large unit. A more practical and commonly used value is enzyme unit (U) = 1 μmol min−1. 1 U corresponds to 16.67 nanokatals.
  
  


Here are some additional useful, simple videos explaining enzyme activity:


How Enzymes Work
Explain factors affecting enzyme activity