I remember, when I was a beginner, being completely confused about what all those ground symbols meant. That was one of my first big stumbling blocks in electronics. The answer is that they're usually nothing but notational: They save you drawing some wires (every ground symbol is assumed to be attached directly to every other ground symbol by a very-low-resistance wire [1]) and more importantly they define your reference voltage (once you've drawn a ground, you can say things like "this point in the circuit is at 3.2 volts", instead of "this point in the circuit is at 3.2 volts relative to Point X".)
---
[1] There are times when the connections from ground to ground have too high a resistance, or when you pour so much current into ground that the ground-lead resistance can't be ignored anymore. Those are called ground loops, and are topics for advanced class. I have a nasty ground loop when I connect my stereo system to my cable TV. It manifests as the sixty-hertz hum from hell.