P-value (probability value) in statistical hypothesis testing may be hard to understand at times. The best way to understand it is as follow. First one needs to understand that in science the goal is to prove that there are no differences between two (or more) sets of data (for example series of parametric numbers derived or collected about individuals, instruments, or other behaving or sizable objects).
Let us imagine two groups with 10 individuals in each group. And we have collected temperature from each person in both groups. One group received aspirin before measurement and the other, the control group, received a placebo (inert tablet). Our goal was to prove that there would be no difference between the two groups (proving the null hypothesis that Aspirin has no effect on temperature).
The P-Value is the probability that the result we obtained (i.e. the difference between the two groups in terms of their temperature as a function of Aspirin) is not merely due to chance. And, thus, the lower the P-value, the lower the probability that the result obtained (temperature differences) is due to chance alone. Here if the P-Value is less than .01 (1%) or .05 (5%) we can be confident that only less than 1% or 5% of our finding can be due to chance. Because our "chance value" is so low, we would reject the null-hypothesis. That is we reject our own intent (hypothesis) that there would be no difference between the two groups. Aspirin did have an effect on temperature and that was not due to chance alone. Only less than 1% (p<.01) or 5% (p<.05) may be attributable to chance alone.