I don't really agree with the term "AI" here, but let's use it for now.

I'll speak for neural networks, and particularly, a method called "supervised learning", i.e. learning where you as a human know the inputs and the desired outputs of the learning data set.

Neural network is just a mathematical model that:

1. takes in some inputs,
2. does some math on these inputs, and
3. spits out an output.

Training the AI is, in simplest possible terms, adjusting the parameters of step 2.

When training the AI, you have a bunch of data where you know the inputs and outputs. Say you want to train the AI to recognize which image has a cat in it. You have a bunch of images, and you, as a human, know which ones are cats, and which aren't. Those images will be used to train the AI.

So, in the process of training you:

1. Give the AI its input (images of cats; and from the perspective of computer software, an image is just an array of pixels each with a particular color)
2. .
3. Give the AI the output, i.e. tell it which images have cats and which don't by giving each image a 0 or 1 value.

Now with known inputs and outputs, the AI tries to figure out the middle step. Similar to how when you've got an equation 3 × X = 6 you try to figure out what X is by asking "what number do I multiply with 3 to get to 6?", the AI tries to figure out "what kind of math do I need to do to a bunch of this pixel data to get to '1'?".

This is done through some mathematical algorithms, essentially by first trying certain parameters and seeing what output it gets it and then iterating with math to get closer to the solution. And through that process, the AI adjusts its own parameters so that, when you give it a bunch of pixels, it can take that pixel data, do math, and the result of that math equals 1 if there's a cat in the image and 0 if there are no cats.

So, in short (and oversimplified), you've got equations:

"image with a cat" × X = 1

"image without a cat" × X = 0

Training is using a bunch of mathematical algorithms on known data to figure out what X is.

Now that the X is known, you can give AI an unknown image so it can do math "X" on it, and figure out on its own whether the image contains a cat.