>>12580964P-value is the probability of getting a value lower than the test statistic. Therefore, if it is smaller than your confidence level (typically 0.05) you can reject the null hypothesis.
There's lots of hypotheses tests you can do for the relation between two sets of data. I guess you're talking about a correlation test, in which case your H0 is ro<=0 if you're looking for a positive correlation, >= if you're looking for a negative one, or = if you're looking for whether there is any at all.
