Swaploit is an exploit for PSP 1.50 to run unsigned code on the device. It was the first method used to take advantage of flaws in the firmware version that allowed homebrew to be launched. However, it required two Memory Sticks and a swap, and if the process wasn't done right by the user, the console could have been damaged.
Some days after Swaploit first appeared, another exploit for the flaws called Kxploit was released. Kxploit is a much safer option and only requires one Memory Stick to work.