I have no idea what they ask on the DAT about the p-value... it's been 5 years since I took the exam and I'm pretty sure they didn't ask me anything about it. If you post a couple sample questions I could see what they like to test you all on.
The p-value represents the probability that whatever result you obtained was due purely to chance. The alpha value is the maximum limit that your p-value can be in order for your results to be statistically significant.
A lot of the time your alpha value is 0.05 which means p < 0.05 is significant.
Say you had p = 0.20. That means there's a 20% chance that the data you collected is what it is by luck. Whatever you were testing in the experiment has no correlation with the results... they just happened to come out that way randomly. There's a 20% chance that happened. Would you be confident that there's a correlation between what you did and what occurred if you knew that 1 out of 5 times the data comes out that way on its own? No.
Say p = 0.02. That means there's a 2% chance the data you collected is what it is by luck. That's a 1 in 50 chance that the supposed "correlation" you found was just coincidence. Would you be confident that there's a correlation between what you did and what occurred if you knew that 1 out of 50 times the data comes out that way on its own? Yes.
There are many tests in statistics that generate a p-value but what I wrote above describes what the p-value represents.