Just to clarify some of the info in this thread; the 'spectrum' of a light source is effectively the wavelengths of the colour spectrum the light source outputs. A continuous spectrum light source is anything which burns (i.e. daylight - the sun, fire, tungsten). 'Continuous' refers to the fact that a light source like this would output a percentage of every colour represented in the colour spectrum.
It's easiest to imagine it as being represented by a graph, with the colour frequency underneath. A continous spectrum light source would look like this (where RGB etc would be represented as wavelengths, measured in Nanometers - Nm):
A discontinuous spectrum light source is generally one which tries to emulate daylight, and they're usually electronic (i.e. light bulb, flourescent tubes). These output as many colours as they can to try and appear as a continous source, but they have wavelengths of colour missing. Again, in graphical form, they would appear:
This would represent your typical household light bulb.
The final one is a Line-Plus continuum source, which would be your electronic flash, or a daylight-balanced bulb. This is effectively a better discontinuous source, in that it tries to represent a larger percentage of the wavelengths.
Note how many more wavelengths are shown to fill the gaps.
The colour temperature of a light source comes from whichever of those wavelengths is the more dominant. A fluorescent tube would show a green cast in photos, as that would be the most dominant wavelength. The human eye automatically converts this, but the camera does not (hence WB settings).
Hope that helps.
*Excuse the diagrams, they were knocked together very quickly in CS3. They're not intended to be accurate in terms of the colours, or the range of wavelengths.