Every time we go to my mom's we see the power plant across the river--and every time, my kids ask, "Why's it called a 'plant'?" And every time, I go, "Uh . . . " At one point I made up an answer--and what do you know, I was right! LOL
Plant is from the Latin planta, meaning "sprout, shoot, cutting" which may be from plantare, "to drive in with the feet, push into the ground with the feet." Which is in turn from planta, "sole of the foot." By 1550 it moved from its first English meaning of "shrub or newly-planted herb" to any vegetation. The verb "to plant" has been around since Old English, just like the noun.
Now, the building--it is fact from the same idea, meaning a building planted in a particular area for industrial purposes. That usage came into meaning in 1789. And interestingly, the meaning of "a spy" is from 1812. =)