A Dyson sphere is a theoretical object that encompasses a sun essentially gathering all of its energy. Freeman Dyson is the conceptualist behind the Dyson Sphere but has actually expressed his disdain of the fact that the hypothetical engineering megastructure was named after him. In fact, to this day, he openly credits the origin of the idea to the 1937 novel Star Maker by Olaf Stapledon and wishes it had been named something else.
In essence, a Dyson Sphere is an immense, solar energy collecting megastructure whose purpose is to power a space-faring civilization, generally associated with a species’s achievement of becoming a Type II civilization on the Kardachev Scale, which is a species which collects and utilizes the power output of an entire star.
In the Star Trek The Next Generation episode ‘Relics’:
The USS Enterprise-D picks up a distress call from the USS Jenolan, a transport vessel that has been missing for seventy-five years. As the Enterprise drops out of warp to respond to the signal, the starship is rocked violently by a massive gravitational field. Although initial scans do not find the source of the field, they trace the field to its center and discover a massive spherical structure, two hundred million kilometers in diameter (about 2/3 of the Earth’s orbital diameter around the Sun). The sphere’s dimensions are consistent with those of the (until then) theoretical structure known as a Dyson sphere.
Source: Star Trek Wiki Memory Alpha
The Dyson Sphere in all its glory will have to excuse the fact of being only the 2nd best thing about the episode, with the best thing being the guest appearance of Montgomery ‘Scotty’ Scott played by James Doohan.