People who are diving without any direct assistance of an underwater breathing apparatus are called Freedivers. Trying to dive at a great depth or being as long as possible underwater is what's freediving all about. It takes a lot of training and special equipment to take freediving to the limits. For example, the freedive fins are longer and more flexibel, freedive masks are smaller and  freedive computer are more easier to control (read: less features) than normal dive computers.