Voltage is a measurement of the difference in potential energy from a particular reference point (usually this reference point is ground, which we consider to be 0V). When a voltage is positive, it simply denotes the voltage potential at the point under measure is higher than that of the reference point. A negative voltage only means that the point being measured is at a lower potential energy than the reference point. You could likewise switch the leads on your measurement device (the point under measure would be your new reference point, and your old reference point would be your new point under measure), and you would now read a positive voltage.
In Fig. 1, Node A is measured at 5V with ground as reference, and Node B is measured at -5V referencing ground as well. Voltage sources like batteries shown here, are measured by the difference in voltage across there terminals. By connecting the positive terminal to ground, you effectively set the voltage at that terminal to 0V. Since there is still a difference across the positive and negative terminals, the negative terminal (Node B) is at lower potential energy than ground (hence negative voltage).
The key points to remember about voltage measurements are that they are relative measurements to a reference point.