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Typically you would use a carrot for eating. However, in certain situations, carrots can be particularly useful as weapons. Take a bite, whack someone, and then pull out your butter sock to finish them off.

If you are referring to the carrot symbol, ^, on a calculator you simply put a number after the carrot and make sure to be aware of your parentheses otherwise it could mess up your calculations. 

For example 

2^2 would be 2²  which is four

However,

Take these two expressions as examples

2^(2) + 2  and 2 ^ 2 + 2

1. 2^ 2 + 2 Could be read by your calculator as 2²⁺⁴  which is 2⁶ = 64
2. 2^(2) +2  whereas 2² + 2 would be 6.

As you can see there a huge importance over where you put the parentheses  and don't put them.

If you mean "caret" being this symbol: ^ it is used to say "to the power of" for example 7^4 is 7 to the power of 4 which equals 2401