She is addicted to globetrotting and has visited every city in South America.

We decided to sell our house and dedicate ourselves to globetrotting until we find a new place to call home.

Its a relatively new phenomenon (in that sense of the word), and couchsurfing is used by many of them for accomodating themselves and other globetrotters.

Globetrotting basically means world traveling.

Globe = world

Trotting = go or walk briskly (i.e. traveling)

Globetrotters don't tend to spend extended periods of time in one place, like an extended vacation. They go from place to place and visit multiple places in one trip - often quite diver places (different countries or even continents).

I'd say it's usually used as a personal noun, i.e. "She's a globetrotter." Alternatively, you could use it as an adjective: "His globetrotting lifestyle is the envy of all of his friends." 

"Globetrotting" usually refers to the rich and well-travelled, so you probably wouldn't describe an immigrant as a globetrotter unless he or she had also lived in several countries before and was quite wealthy. For example: "Before returning home to take over his father's company, Thomas was known as a bit of a globetrotter, as he had lived in 6 different countries and visited 30 more before he turned 30."