Purpose of Variance I know how to calculate variance, in probability and experimental data ect but, what I cant seem to understand is the real world application of it. And just wondering if someone could give an explantation of it importance in statistics and experimental data, by giving an example.

For Practical Example I can say,
Let's say that you've to a coke plan a party in your house, there are 100(s) of guest coming to your house. You want to give them a Coca Cola but the problem is that each of them has their different capacity. A kid might need just a glass, but an adult would need more than that.
So, in this case, finding the mean would help you in imagining a person equivalent to someone in the party and finding the right amount.
But, after the party, you took the data and a part of the people didn't have any drink, rest had just a glass and rest had more than a couple of glasses. (Probably some really liked that! :P)
Since you had the correct mean, you didn't fall sort of drinks.
But, when you noticed that variance (it tells the mean of variation) you found that it was more than mean.
Why? It tells that those who took the drinks, took too much and who didn't take were very less. 

More the Variance $\iff$ Who liked the drink took more and who
  disliked, took very less. But
Less Variance $\iff$ Most of the people took it nearly to your
  estimated amount.

Variance = Measure of the variation of the quantity around the central tendency.
Mean - the amount equivalent to each person who takes the drink.
Variance - the amount of drink you gave for each time (or size of the glass)
