Human flight is possible, but only with the help of technology. No matter how fast a person flaps her arms, the human body is not capable of flight without the additional lift provided by synthetic wings or propulsion systems, like jet packs or squirrel suits.
Sustained human flight has been a dream for thousands of years. Leonardo Da Vinci drew fantastical and ingenious schematics for flying machines, including versions of a helicopter. But it wasn't until the end of the 19th and the first years of the 20th century that human flight was finally achieved. The Wright Brothers famously proved the concept at Kitty Hawk in 1903.
If a person wants to fly, the easiest way is to learn to operate an airplane. There are, however, alternatives to airplane flight. Sky diving and base jumping offer the opportunity to literally fly through the air. In the case of base jumping, modern thrill seekers have taken to using what is known as a squirrel suit: a winged body suit that allows the jumper to catch thermal air and "fly" along ridges and canyons, instead of falling straight down.