What does it mean for a function to be computable?

Although informally a function is computable if its values can be calculated, Alan Turing, Alonzo Church, and Kurt Godel each had formal definitions of computablility, namely Turing Machines, Lambda Calculus, and general recursive functions.  When it was shown in the Church-Turing thesis that these three formulations are equivalent, it became more clear that they could be used as a formal definition of computability.