Quoting https://en.wikipedia.org/wiki/Kleene%27s_T_predicate:

The ternary relation T1(e,i,x) takes three natural numbers as arguments. The triples of numbers (e,i,x) that belong to the relation (the ones for which T1(e,i,x) is true) are defined to be exactly the triples in which x encodes a computation history of the computable function with index e when run with input i, and the program halts as the last step of this computation history.

In other words: If someone gives you an encoding of a program, an encoding of its input and a trace of its run, you can check with a primitive recursive function whether you have been lied to.