Positive Testing: Testing the application functionality 
with valid inputs and verifying that output is correct
Negative testing: Testing the application functionality 
with invalid inputs and verifying the output
Difference is nothing but How the application behaves when 
we enter some invalid inputs
Suppose if it accepts invalid input the application 
functionality is wrong

positive test: testing aimed to show that s/w work ie with 
valid inputs.this is also called as "test to pass'
-ve testing: testing aimed at showing s/w does't work. 
which is also know as 'test to fail"
BVA is the best example of -ve testing.

Example of positive Testing is u have one login form where 
u have fields like name , password etc and now u r checking 
for name field u enter right character(VALID DATA) in that 
name field this is called positive testing and when u r 
entering wrong data(INVALID DATA) in that name field is 
called negative testing.