Complex sentence: A key part of the proof was a mathematical definition of a computer and program, what became known as a Turing machine; the halting problem is "undecidable" over Turing machines.
Split into simpler sentences: A key part of the proof was a mathematical definition of a computer and program, what became known as a Turing machine. We say that the halting problem is "undecidable" over Turing machines.