A passive radiator is similar in function to a port, it has a 'resonant frequency' in the box that extends the output of the subwoofer. It operates over a narrow bandwidth, and can fit in places a normal port cannot: IE, a small box with a deep tune that would require a long, large diameter port that will not fit in the box.
Downsides are steeper roll off than either a ported box, and higher cost. ( about 30 db/octave for a PR box, 24 db/octave for a ported box, and 12 db/octave for a sealed box )
Plus: can tune a small box deep without excessive port compression and / or port chuffing from an undersized port.
Most passives are adjustable by adding weight, and good ones aren't cheap at all. The less expensive ones have less excursion and usually can't take a lot of weight, as the spider and the surround won't support that.
There are modelling programs that can help you model passive radiator or port behavior and tune a box, such as "WINisd" from linearteam.