The null hypothesis is that the average high temperature in december is 45 degrees. if someone reports that the average was 52 degrees and that the p-value for this is 0.036, what does the p-value represent?

P-value approach is used to take a decision to reject or accept the null hypothesis as indicated below:
REJECT the hypothesis, if p-value FAIL TO REJECT the hypothesis, if p-value > the alpha value.
Alpha value represents the level of significance 
If alpha value is NOT indicated: alpha = 0.05 can be assumed 

REJECT the hypothesis, because p-value (0.036) < the alpha value assumed which is 0.05