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In statistics we tend use the 'hat' notation to imply a statistic. We designate P to represent the proportion in the population. Because P is unknown and unknowable we use Phat to designate the proportion in the sample. Suppose 30 out of 100 people in my sample support Trump. P = unknown and unknowable.
First and foremost, a p value is simply a probability. However, it is a conditional probability, in that its calculation is based on an assumption (condition) that H0 is true. This is the most critical concept to keep in mind as it means that one cannot infer from the p value whether H0 is true or false.