Meaning of "Grounded" In my opinion, "grounded" means having the same potential as the potential at infinity, which is usually set to zero. Now if we consider a conductor inside a uniform electric field, what is the meaning of a conductor being "grounded"?
 A: In common usage "grounded" means 

Connected to a conductor which I have arbitrarily deemed to be at an electric potential of 0, and which has such high capacitance that you can assume it never builds up any charge.

Of course, the word comes from the convention that we literally use the ground as a potential reference. In any experimental physics building there's a huge spike of metal that's literally driven into the ground. That spike is big and fat so that it's resistance is really low. By connecting one of the wires of each piece of equipment to this spike you are guaranteed that they are all using the same voltage as their reference.
This is important because current flows through that "ground wire." If the resistance is not small then there will be a voltage difference between different points on the ground reference, which means that different pieces of equipment each measuring the same voltage would report different numbers.
There are other considerations, but that's the essence.
A: in my opinion, and based on convention, grounded means the system won't build up any potential.
Say you have one end of battery connected to a sphere - not grounded, and sphere builds up a potential difference relative to the other terminal.
Now, while the system intact, you connect the sphere to the other terminal of the battery - grounded, the sphere won't build up potential difference now.
So, in your question, I believe the conductor is connected to a ground supply.
