It's about as old an expression as a "half and half" session, which of course means a blow job and then sex.

 
Actually you don't have to actually finish in all three holes, just visiting each one during your session qualifies as "around the world"

...and i disagree...three finishes one in each area is the only way a "REAL AROUND THE WORLD"is complete....whats the point otherwise....Im open to help the newbie ladies who need a personal "travel guide"  

Similar to what GaGambler said, it referred to a session that included accessing several parts of the woman's body in one session, or going through several sexual positions in one session. I even remember how I personally learned of it. I was watching a (mainstream) movie and a woman, I believe she may have been a prostitute, said the term to a guy, he didn't know what it meant, so she explained it to him. It apparently cost more than a quick wham, bam, thank you, ma'am because it was more activity taking a little more time.  I can't remember what the movie was nor who was in it.

I doubt the term is still in use today in that same meaning, because as we can see from TER as one example, the average session includes all of that. Today's slang may have other definitions for around the world.

In 1979 one of the worst Bond movies was released, Moonraker.

Bond girl's name was "Dr. Holly Goodhead" played by Lois Chiles.  She hated the characters name.  

What she hated even worse was the last line in the movie.  She and Bond are ready to do the nasty floating in zero g.  

She say's..."Take me around the world James".  

So there you have it.