Understanding of neural networks, how do neural networks work?

The neural network saves the input and output of the training data, and takes the data to find the corresponding data when testing. So what artificial intelligence is it talking about? Isn't this just looking for similar data from historical data? Isn't it based on experience?
Obviously this is not the case. If it is really like the above, then there really is no intelligence!
How does it embody intelligence? The purpose of neural networks is to predict the unknown through the known.
There is such a small example, a function unknown function y=t(x) has two variables, where the independent variable is x and the dependent variable is y, t(x) is called the actual function or the true function. The neural network is y=h(x). Our purpose is to take some sample points from the unknown function to train h(x) so that h(x) approaches t(x). It should be close during training and tested. Time must be close.
Then, during training, h(x) must be close to t(x) through methods such as least squares, and during testing, some data is not available during training. How to make these data close to t(x)? Is the key to neural network intelligence?