Roughly translates to "do the
math in an unthinking way".
I'm not sure why this hasn't been noded yet, since there's so many engineering students or engineers here. Maybe it's no longer used. But,
when I was in college studying engineering, this was a common phrase amongst jaded, apathetic students struggling to finish their homework assignments. "Plug and Chug" meant that you were simply taking an equation and plugging the numbers into it and getting another number as an answer, even if you didn't understand the concepts behind the equation or what the answer meant. The intense pressure of engineering school meant that you ended up doing this quite a lot, especially if you also wanted to have a life outside of school.
Sometimes I think people with an engineering background learn to look at all life's problems in this way. Which might be a good or a bad thing. Occasionally you get into a situation where you will never understand the underlying reasons for things, but if you can boil down the problem to inputs and an output, you can often get a solution that works. Of course, your mileage may vary. This can often be a very dangerous way to look at things, especially interpersonal problems and other things involving those pesky humans.