Grounding is for your electrical system. In normal operations, in a basic sense, electricity comes into a device on the hot wire, and leaves on the neutral (not really, but for these purposes the idea is just fine). The ground is there to provide an alternate return path should something go awry (such as a metal part coming in contact with a hot) allowing the fault to trip the breaker.
A bond connects two different conductors that would not otherwise be connected, so that they are at the same electrical potential. If you shuffle your feet across the carpet, you will built up an electric charge in your body - which in an of itself does nothing. But then you touch a metal doorknob and you get a shock. Why? Because you were at a higher potential than the knob, and when you touched it, the potential equalized. It had nothing to do with your household electric service. Now, if you took a piece of wire and connected it to the doorknob and held the other end in your hand, you could shuffle around on the carpet all day long, and when you touched the knob, you would not feel a shock, because you are BONDED to the knob. The bonding allows the electrical potential between you and the knob to remain equal.
To bond a pool, you connect everything in the area that can conduct electricity together with a wire. The metal pool wall, the earth, the water, the metal handrails, the metal pump housing, etc. These things can build up different electrical potentials, just like your hand and the doorknob. However, in some cases, the difference in potential can be quite large (usually because of a problem with the electric service in your area). The earth could be a high potential and the pool water at a low potential (because they are not connected, the water is in a big vinyl bag) but you can walk on the ground with no problem. But then while standing on the ground you stick your hand in the pool, and you get zapped, just like the doorknob, but bigger. Bonding connects all of these things together, so that they all become the same potential and you do not get a shock when bridging between two (of more) of them.