Special Students is a general term referring to the people receiving special powers after being exposed to B Power. The great majority of the demographic affected by B Power are teens or in their early twenties, and the power usually wane as they grow older. Thus the generalization of "Students" even though not all of them are actually students in school.
The ability of Special Students come in myriad forms. Somebody may have super strength, somebody else may be able to help plants grow faster; somebody may be able to always roll any dice result, and somebody may be able to sing any song backwards after only listening it once. The one thing in common is that special ability uses B Power, and Special Students who depleted their B Power become like normal people. Special Students typically replenish B Power through B Stones, or sometimes directly via B Crystals.
The original Japanese 特体生 ("tokutaisei") is a homophone pun on 特待生, which literally means "Special Treatment Students". The term refers a program where schools would offer scholarships or other benefits to students with great athletic or academic standings, improving the schools' reputation by having strong students. The pun alters the second kanji from "Treatment" to "Body", so the new kanji literally means "Special Body Students".