A bioassay uses a living organism--usually a plant or a bacteria--as a test agent for the presence or concentration of a chemical compound or a disease. The idea is to choose a test agent that is very sensitive to the condition you are testing.
Have you ever read about how miners took canaries down into mines to act as early warnings of gas leaks? Because canaries are more sensitive to gas than people, the birds reacted to very small amounts of gas and gave miners a chance to escape. You could say canaries were a bioassay for underground gas.
Different plants are often used as bioassays because they respond in a predictable way and are often very sensitive to the condition that is being tested. A standard toxic dose--the level at which no seeds of the bioassay plant sprout or all the plants die--is established as a reference point. Then samples are tested and compared to the reference standard.