The precision of the findings.This is the range within which the predicted means of population may lie.
A confidence interval is the range of values within which the "actual" gods-own-truth result is found. Essentially, a CI of 95% means that if a trial was repeated an infinite number of times, 95% of the results would fall within this range of values.
The probability of the observed result arising by chance
The p-value is the chance of getting the reported study result (or one even more extreme) when the null hypothesis is actually true.
For example, if your findings are that 1g of oral cyanide kills 95% of swallowers, a p-value of 0.05 would suggest that if cyanide was completely harmless and you repeated your experiment an infinite number of times, your results would be reproduced in 5% of those experiments.
Thus, a very small p-value - say, 0.0001- gives rise to the impression that the results are valid, because it suggests that if the investigator's hypothesis was in fact completely wrong, the chances of arriving accidentally at their "mistaken" results would be 0.1%.