^ often means raised to the power of. Like 2^2 would mean two squared or four.

Now a bunch of ^'s in series would mean the exponentiation is done iteratively much like eponintiation is iterative multiplication and multiplication is iterative addition and addition is iterative counting.

For Example 2^^2 would be two squared squares or 2^4 or 16.

2^^^2 would be 2^32 or 65536 and 2^^^^2 would be a what I like to call a huge fucking number.

more can be found here: http://mathworld.wolfram.com/PowerTower.html

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Well sir that seems to be someone else's problem.