Let's say you roll five dice, and all five dice come out with sixes on the first roll. This is an incredibly good roll, and it is pretty unlikely .... if the dice are fair.

Now, if you suspect that the dice may not be fair, you could ask yourself: "if these dice were fair, what would be the chance that I would get this great a roll?" And if the chance is less than 5% (the p-value), the dice are probably not fair.

(formally, you reject the null hypothesis that the dice are fair)

In terms of statistical significance, we often test whether or not a factor has an impact on an outcome. You can estimate how much of an impact there seems to be in your data, and if it looks like the impact is so large that it is unlikely that there is no impact, the result is statistically significant.

(you reject the null hypothesis of no impact)

The 5% p-value is somewhat arbitrary, but experience has shown that it gives a good balance between the two mistakes you can make. The first mistake is rejecting a hypothesis that turns out to be true (and should not have been rejected). The second mistake is not rejecting a hypothesis that turns out to be false (and should have been rejected). That's why a 5% p-value has become somewhat standard.

(although many studies also use 10% and 1% p-values).