Response: 

The p-value or PROBABILITY value, for a given statistical model, is the probability that when the NULL hypothesis is true the statistical summary would be equal to or more extreme than actual observed results. If we refer to figure 7, assuming a standard normal distribution of a population of data, the probability DENSITY is represented for each outcome and computed under the null hypothesis. The p-value is the area under the curve past the observed data point. 

By convention, p-value is commonly SET to 0.05, 0.01, 0.005 or 0.001 etc. 

We have to note that,  

Prob (observation | hypothesis) <> Prob (hypothesis | observation) 

i.e. the probability of observing a result given that some hypothesis is true is not equivalent to the probability that a hypothesis is true given that some result has been observed. 

If the p-value is too small, the higher is the statistical significance since it indicates to the investigator that the hypothesis under consideration MAY not adequately explain the observation.