To understand intuitively or by empathy.
That's a rough definition. WIkipedia will, as usual, gives a more elaborate description.
Etymology: coined by Robert A. Heinlein in his 1961 novel Stranger in a Strange Land.
I'm curious to know how common the word is today. In my college days (over 25 years ago, and roughly when I read Stranger in a Strange Land), people I hung out with used it all the time. In my brief stint of hardcore software development after that, it was also common. Seems like I've heard it rarely in the last decade, but I'm not sure if it's become less common or if it's because I run in different circles these days.