How can a conductor be grounded yet there are induced charges on it?

A classic example for the method of images is the following, quoted from Griffiths's Introduction to Electrodynamics, page 121:

"Suppose a point charge $q$ is held a distance $d$ above an infinite grounded conducting plane. Question: What is the potential in the region above the plane?"

Griffiths continued on solving the example using the method of images setting V=0 on the plane as one of the boundary conditions saying "since the conducting plane is grounded".

Now, of course there will be an induced surface charge density. My question is, how can this be since the plane is grounded?

Does the word grounded have different meanings? sometimes it means not charged and the others it means the potential there is 0?

-
can you point us to a reference were by "grounded" the author's mean something different than a potential value or zero? –  luksen Oct 17 '11 at 12:55
@luksen It is from Griffith's, I have edited my question to include the reference. –  Revo Oct 17 '11 at 13:17
Griffith uses that "grounded" means V=0. I'm interested where you read that "grounded" might mean "not charged" as you state in your last paragraph. –  luksen Oct 17 '11 at 14:02
At least in the part you quoted, there is nothing to suggest that "grounded" means anything other than "at zero potential." –  David Z Oct 17 '11 at 20:30
"Grounded" is not the same thing as "neutrally charged". –  endolith Nov 16 '11 at 22:38

Think of the ground plane as being an infinitely big electrical conductor, initially uncharged.

We bring in a (say positive) point charge close to the surface of the ground plane. An negative image charge is induced on the surface near the point charge, and since the net charge on the ground plane is zero, an opposite positive charge is pushed off "to infinity".

Now suppose we bring a positively charged conductor up to the ground plane, and then connect it electrically. The positive charge in our conductor gets discharged and cancels the negative induced surface charge, but the positive charge that had been pushed off to infinity is still out there and gets redistributed. Since it is a finite charge distributed over an infinite body, there is effectively zero charge density.

-