Positive Testing is the process where the system validated against the valid input data. In this tester always check for the only valid set of values and check if an application behaves as expected with its expected inputs.
Positive Testing always tries to prove that a given product and project always meets the requirements and specifications. Under Positive testing is test the normal day to day life scenarios and check the expected behavior of the application.
Negative Testing is testing process where the system validated against the invalid input data. A negative test check if an application behaves as expected with its negative inputs.
Negative testing is a testing process to identify the inputs where the system is not designed or unhandled inputs by providing different invalid. The main reason behind Negative testing is to check the stability of the software application against the influences of the different variety of incorrect validation data set.