In mathematics, the square root of -1.
There is no value in the real numbers which, when squared, gives -1. So mathematicians just invented another symbol to represent it, and called it a new number. It's happened before - there is no integer which, when multiplied by 2, gives 1 - so mathematicians invented a symbol for it, ½, which generalised into the whole concept of division and rational numbers. There is no natural number which, when added to 1, gives 0 - so mathematicians invented a symbol for it, -1, which generalised into the whole subtraction and negative numbers idea. iota is just another step on the ladder of expanding the expressiveness of mathematics, encompassing an ever-increasing set of values. iota itself generalises to give us a whole set of imaginary and complex numbers.
Iota, when written properly, does not have a dot over it - unlike the letter 'i'.