Why should a circuit be grounded?
The term "ground" can mean different things.  When a circuit is looked at locally, ground is simply the one net someone picked to call 0V so that all other voltages are understood to be relative to it.  Voltage is after all a relative concept.  There is no such thing as 20V absolute, only 20V here with respect to there.  "Ground" is a handy short form for a common there so you don't have to keep saying it.

Such a ground is often chosen to be the negative supply voltage.  That makes other voltages positive, which just makes things mentally easier.  In general you try to chose ground as the point in the circuit signals and the like are referenced to by individual subsections.  Usually there is a clear and obvious choice.  Sometimes you just have to pick one.

The other "ground" refers to real earth potential, or at least the potential of the general surroundings.  This matters when power and signals are coming from or going outside your little circuit.  For power and saftey, you have to assume a user could be tied to this ground, and you have to make sure you don't have a dangerous potential to ground to avoid zapping someone.  Earth ground can also matter for radio systems since some types of antennas actually use the earth as part of the overall antenna system.