Negative testing is a procedure which validates that the system works smoothly in case of any invalid inputs.
For example, in case the user enters any invalid data in a text box, the system should display a proper message instead of the technical message which the user does not understand.
Negative testing is different from positive testing in a way that positive testing validates that our system works as demanded and examines the test results with the expected results.
Most of the time scenarios for negative testing are not mentioned in the functional requirement documents. As a QA we have to recognize the negative scenarios and should have provisions to test those.