One of the hobbyhorses that John W. Campbell started to ride in the 1950s (others included the Dean Drive and (ptui!) Dianetics). They were dressed more scientifically than the Shaver Mystery and probably (unlike the Shaver Mystery) were in large part an honest attempt on Campbell's part to widen the bounds of scientific orthodoxy, but in the end they were garbage.
Campbell's insistence on stories that played to his own unorthodox orthodoxy hastened the fall of Astounding from the pinnacle of SF to just another prozine. Not all the psionics stories were bad, of course, but they tended towards a dreadful sameness.
Psionics was, basically, a scientific dress on magic: Using the power of the mind to accomplish things in the real world without the mediation of the body. It included telepathy, teleportation, clairvoyance, and the the direct manipulation of material things.