Bespin is a giant gas planet with a breathable atmosphere in a similar way that Jupiter is. There are communities on Bespin where people collect Tabianna Gas. One of the cloud Cities is administered by Lando Calrissian, an old friend of Han Solo. Lando Calrissian became the administrator after winning it in a game. The City provides the climax to the `Star Wars V - The Empire Strikes Back` where Han Solo is placed in carbonite.
Cloud City had until Darth Vader turned up to capture Han Solo been of no interest to the Galactic Empire. The planet is situated in the Outer Rim, away from the central core of planets including Coruscant.
It only appeared in The Empire Strikes Back, excluding any cartoons and books you may have read or seen. It is where Darth Vader set up a trap and froze Han Solo to be frozen in carbonite so that he could be transported to the desert planet Tatooine for Jabba, the Hutt by the bounty hunter Boba Fett. Han Solo had gone to the planet to seek sanctuary from the Empire as he believed Lando would help him out. Whilst seemingly friendly, Lando betrays Han Solo who hands Han over to the Empire.
When Luke Skywalker who is having a training session on Dagobah with Yoda sees what he believes is happening, Luke abandons his training and journeys to Bespin. On Bespin, it is where Luke Skywalker discovers that Darth Vader once used to be his father Anakin Skywalker. Darth Vader offers a position to his son and together they could both rule the galaxy together. Luke rejects the offer from his father and is subsequently falls to his seemingly death but manages to save himself after managing to grab hold of something before calling out to Princess Leia to save him.