Dreaming about dyson spheres --
Dyson's sphere was the product of considering the classic physics problem -- the heat death of local systms, and eventually, the entire universe.
Cosmologists started thinking about this along with the evolution of understanding about how stars in our universe represent the ultimate primary energy source. We realized that a star is basically an engine that runs on the matter-to-energy conversion process of nuclear fusion. Like all other such processes, subject to the second law of thermodynamics, these fusion engines will eventually start running out of gas -- or hydrogen, as the case may be. Some day the stars will cool off and die.
If we are thinking on an extended time scale, just casually tossing around billions of years, we can project a time when human civilization might be threatened by this approaching "heat death". Since we require the energy that comes from the stars to fuel our own existence, when the sun starts running out of gas, so will we.
Dyson figured that one way to forestall the inevitable demise of human culture would be to maximize our collection and use all of the energy coming from the sun. Right now, most of the sun's energy production radiates out into space. Dyson envisioned a construct like a shell, surrounding a star, which would effectively intercept nearly all the solar energy coming from the sun. His original idea was to construct a huge array of moderately-sized platforms, something resembling the solar panels that some use for generating power, only on a collosal scale. These platforms would orbit the sun at about the same distance as the earth's current orbital path, effectively surrounding the whole diameter of the star. Later development of Dyson's theme resulted in the idea of a solid spherical shell construct that the term "dyson sphere" now evokes.