Sometimes defined as narrowly as "supernormal perceptual states" (say for Buddhists who don't go in much for parlor tricks), a siddhi can be just about any very unusual talent developed through meditation, yoga or awareness. Siddhis can also be triggered by drugs or unusual mental states. A standard example of the uselessness of many siddhis is the talent to reverse colonic peristalsis, so that the practitioner can suck water up their anus. This saves money on colonics and can impress naive villagers, but it's not much payoff for a few decades of mantra-bashing.
Yogic "flying" (really hopping) through TM is another siddhi - but again, is the purpose of spiritual attainment to get the equivalent of frequent flyer miles?
An example of a more useful siddhi is the ability to see with sound, that is, to see in total darkness or while blindfolded. A minority of blind people develop this talent without training, and it can also be a "spiritual" attainment. In either case the part of the brain normally used for vision is engaged, and the picture that emerges is perceived in black and white precisely as if it were very dim night vision. At least some ambient sound must be present, and widely placed discreet sounds such as rain falling on a roof are ideal. Resolution is not more than one inch or a half an inch at most, so if you obtain this siddhi beware of walking into the edges of doors precisely lined up with where you're going. (It turns out Siddhis aren't really magic.) I was once able to escape from a fairly long and complex cave with just one small exit after all my light sources failed with this siddhi, so I count it as a useful. As it happens, I obtained it in part through wandering around with my eyes closed as a bored child, after I'd read all the books the library would let me borrow in a week. Librarians take note.