Transform functions are any function say X that map to itself.
There are different transforms as below and they tend to solve various real time scenarios from designing electrical circuits to solving signal systems ,from communication engineering to nuclear engineering.
- Laplace transform
- Fourier transform
- Mellin transform
- Hankel transform
We can study properties of a radioactive substance using Laplace transforms.
You can find more examples of Laplace Transform here :
All the above wikipedia examples are real time scenarios.
Your question is a good one ,but it is broader since there are different dimensions in Transforms.