Generative AI tools are those that produce text, code, audio, images, and other media based on a user's prompting. Some examples are ChatGPT, Stable Diffusion, Midjourney, Github Copilot, Google Bard... and many more!
These tools have been trained on large amounts of data. Training refers to passing data to a model so that it can extract features related to the data and make connections between data points.
Let's take an example of predictive text for email or texting. Those AI models have been given enough text that when they see you type "Hope you are doing", the model can reasonably predict the next word is "well". The word is then suggested to you in order to complete your statement.
With a tool like ChatGPT a similar premise exists. A very large amount of text (about 570GB of compressed plaintext data for GPT-3, according to Brown et al., 2020) has been given to this model, so when you ask it a question it is able to decide what a highly probable reply would look like and responds with this very real seeming answer.