to try to find out about something by testing. We are testing for weak places in your roof. That's the noise you hear up there. They are testing for some sort of infection.
to apply a test to someone or something to try to determine something or identify something. They tested me for all sorts of diseases. Ken tested the roof for weak spots.
To administer a test to someone or something in order to determine the presence of something: The technician tested the blood sample for leukemia. The doctor tested the children for head lice. This procedure tests for the presence of harmful substances.