If I understand your question correctly then the target function is a function that people in Machine learning career tend to name it as a hypothesis.

In machine learning, you are given a lot of data and its target value (sometime called class or label or answer).

Specifically, the target function can only be inferred in a Supervised learning task.

A target function maps data to its target value such as if you have picture of a digit, the function then receives that picture as the input and spit the digit value as the output.

The process of finding that function is called learning or training.