OpenAI o3 is one of OpenAI's reasoning models. These models spend more time thinking through a problem before answering, which makes them useful for tasks such as maths, logic, coding and multi-step analysis.
This listing points to OpenAI's page about early access for safety testing of the model. Access generally comes through OpenAI's own products and developer platform on paid terms. It is best suited to people who need careful, structured answers rather than quick casual chat.