In technical terms, ChatGPT is a gateway to the GPT-3 large language model using natural language prompts. GPT-3 is a deep layered transformer predictive text model trained on a massive amount of text with almost five billion tokens.
In English, ChatGPT processes natural English language speech into something that GPT-3 can understand and give you the resulting text. GPT-3 is a collection of math equations that a series of computers spent several months learning so that it can take in a group of words (as long as those words are within the 500 billion words it recognizes), run some math on them, and produce some more words.