According to Alan Turing "Any problem for which algorithm exists, turing machine will exist for that problem."
Anything that can be performed by existing digital computer can also done by using Turing Machine.
This is a hypothesis because noone has come up with a problem solvable by algorithm for which a Turing Machine cannot be written.
And from 1930 till today nobody is able to prove that Turing Thesis is wrong.
Turing Thesis Correctness
To prove Turing Thesis either take all the programs(number of programs are infinite) which exists and design Turing Machine for every program, which is a very tedious task or one should come up with a problem for which an algorithm exists but Turing Machine cannot be written.
But later did not happen till date and there are very few chances that someone can do that.
Turing Machine is accepted as definition of "mechanical computation" or "Computer".