p - value is used in hypothesis testing. It reveals the probability of 'chance' to be responsible for the difference. The less the p value the less the probability that the difference is due to chance. Conventionally, a cut off of 5% or 0.05 or one in twenty is considered for saying that there is a statistically significant difference. But, always keep in mind that the difference in 0.049 and 0.051 is not great. The probability that the difference is due to chance is 4.9% and 5.1% respectively in the example given in the earlier line. So they are telling nearly the same story. But going by our cutoff of 5%, one is statistically significant and the other is statistically not significant. Human judgement, common sense and experience should prevail for interpretation of the result. One more word of caution: Increasing the sample size tends to magnify the differences and chances for finding a statistically significant difference increases.

95% Confidence interval arrived from our sample is the probability that the population value lies in that interval 95% of the time. The condition is that the sample should be representative of the population.