Electricity is the flow of positive or negative charges in response to electric forces (an electric field). Static means something is not moving, but there is still an electric field.
What is happening is normally positive and negative charges occur in equal amounts everywhere, so there is no net charge. We say they cancel each other out. If you have more of one or the other, then there is a net charge (an imbalance, as your text states). Since opposite charges attract, another charge would feel a force towards this imbalance. Similarly, the imbalanced charge would feel a force due to other charges surrounding it (ones that aren't cancelled out). If you live in a dry climate you may know the sensation of your hair standing on end after rubbing a balloon on it. What happens is each hair has some extra charge deposited on it, and all these charges are repelling eachother, taking your hair with it.
We say it's static because the charges can't go anywhere. This is because the extra charge displaces the charges nearby it, pulling the opposite ones closer and pushing the same ones farther away. What's important is that it can't push these other charges very far (the material is not a conductor). We say it "polarizes" the material.
Even though the net charge of one of your strands of hair might be negative, and be repelled by other strands, the extra electrons have surrounded themselves with positive charges and are "stuck" in a sense. This is why you need friction to cause an imbalance of charges. You are overcoming this stickiness.
Now if you brought a conductor (e.g., metal) to the material, the charge can attach itself to the metal in the same way, (polarizing the material and then pulling itself towards opposite charges) but because charges on conductors can move around, the extra charge can flow more freely. The charge is still "stuck" to the conductor, but can move around inside the conductor.