VaR

Let me give you a very basic example to explain the idea behind it.

Suppose I told you that I have $10000 in my bank account and I am thinking of making an investment the returns of which are uncertain but might mean I end up with a much higher balance or a much lower balance.
Using standard deviations and normal distribution I have calculate that the probability of the balance falling below $2000 is only 1%.
Provided that I can accept a balance as low as $2000 then (using VaR) then I will take the risk and invest. (I may end up with less than $2000, but the chances are so low that I am regarding it as more or less impossible).

Obviously that is only a simple example, but banks use it in the same sort of way.

However, the huge problems are that it assumes that the returns follow a normal distribution and there is no reason why they should.
Secondly, it ignores the fact that however small the probability is of falling below the limit, if it does happen then it could result in the bank collapsing (and even though it might happen only once in 100 years, the one year could be next year!)