I'm not very familiar with this specific term, but do know intermediate Japanese. "Floating world" seems to be a direct translation of the two characters: 浮 for "floating" and 世 for "world". However, the main definition for this word online is "fleeting life" or "this transient world", similar but more natural in English. Interestingly enough, the fourth entry in the definition is "(the world of the) red light districts". This final definition certainly matches the Wikipedia article and is hinted at with "fleeting" and "transient", suggesting to make the most of pleasure with your limited life.
What is the main definition, especially with respect to Ukiyo-e, 浮世絵?