An intuitive interpretation of Negative voltage
You could consider the voltage a bit like floors on a building. A numbering system used in many places in Europe defines that the ground floor is 0 or G, that floors above it are numbered positively and numbers below it are negatively. You now have the option of measuring everything relative to ground (the floor number) or measuring the difference in level between any two floors (the potential or voltage difference).

In the left image above our man is standing on Floor 2 relative to ground. The electrical analogy is that some point on the circuit is connected to ground / earth and by convention is zero volts and all voltages (heights) are measured relative to this.
An 'all above ground' building will have no negative floors. A bunker or underground car-park will have no positive floors.
If the building is launched off into space he has no ground reference and is free to number the floors any way he wishes, including have Floor 0 at any arbitrary point. This is analogous to having an electrically isolated circuit with no ground connection in that we can call any point 'ground'.




simulate this circuit &ndash; Schematic created using CircuitLab
Figure 2. Two 1.5 V cells with three different reference points.
Hopefully Figure 2 makes it a bit clearer. Depending which point we assign as reference (GND) the other points' relative voltage changes.