Something that is transformed from one state or form to another has had a conversion. The twentieth century saw the conversion from outhouses to indoor plumbing. You may oversee the conversion of your attic into an extra bedroom.
The noun conversion can be used to describe some very specific transformations. If you exchange euros for dollars, you have made a monetary conversion. If your Canadian friend tells you, "It was warm today! It got up to 28!" and you figure out that 28 degrees in Celsius is the same as 82 degrees in Fahrenheit, then you have made a mathematical conversion. If you change your religion, you've had a religious conversion.