The slider represents the colour temp of the light source the scene was shot under. That information is needed to make white appear white.
With light indeed, a 2800K light is a lot warmer than a 5600K light. But this is white balance - so say you shot a scene with 5600K light. 5600k light is pretty neutral to a silicon sensor, but 2800k light is not, it's very red (blue deficient) so if you have your 5600k scene and tell the raw development software via the white balance slider it was shot with 2800k light, the result will be very blue because the software is gaining up the blue to white balance a 2800k lit scene which will be very blue deficient.