Artificial intelligence, usually shortened to AI, is software that performs tasks which normally need human thinking, such as understanding language, spotting patterns or making predictions.
Most of the AI you meet works by learning from examples: developers train a model, which is simply a program fed with large amounts of data, until it can recognise the patterns on its own, and this learning process is why the field talks so much about machine learning, a common way of building AI.
You already use AI every day, probably without noticing, because predictive text guesses your next word, your email app quietly moves suspected spam out of your inbox, and Google Maps estimates traffic from what other phones on the road are reporting. ChatGPT answers questions in plain language, and generative AI, meaning AI that creates new text, images, audio or video, now drafts documents and produces pictures from a short description.
The terms sit inside each other like boxes, where AI is the whole field, machine learning is one method within it, and generative AI is one kind of machine learning, so whenever a tool writes, draws or speaks, that is generative AI doing the work.
This is as much theory as you need to begin, because using these tools well depends far more on clear instructions, your own judgement of the output and care with private data than on the mathematics running underneath.