While it's a very formal and literary term, 乾坤 is alive and well in modern Mandarin, primarily through powerful idioms (成语, chéngyǔ). You will rarely hear it used alone in casual conversation to mean “the world” (for that, you use 世界 (shìjiè)).
In Idioms (most common use): It is used to convey a sense of immense scale, power, and fundamental change.
扭转乾坤 (niǔzhuǎn qiánkūn): “To reverse Heaven and Earth.” This is the most common usage and means to turn the tide, to reverse a desperate situation, to make a dramatic comeback.
颠倒乾坤 (diāndǎo qiánkūn): “To invert Heaven and Earth.” This means to turn things upside down, to subvert the natural order, or to confuse right and wrong.
另有乾坤 (lìng yǒu qiánkūn): “There is another Heaven and Earth.” This describes a situation where there's more than meets the eye; a hidden world or a surprising depth behind a simple facade.
In Literature, Film, and Wuxia: The term lends an epic, almost mystical quality to descriptions. It is famously used in the name of a fictional martial arts technique, 乾坤大挪移 (qiánkūn dà nuóyí), or “Heaven and Earth Great Shift,” from Jin Yong's novels. This usage has cemented its “cool” factor in modern pop culture.