Measuring DC offset.

Out of curiosity, I checked the DC offset on my solid state amp. With my digital multi-meter, the left channel fluctuated between minus 8.5mv to minus 10.5mv. The right channel fluctuated between positive 3.5mv to positive 6.5mv.

Both the inputs from the preamp and the output to the speakers were disconnected.  The amp had been warmed up for 15 minutes.   What do those results mean?

The measurements are meaningless without a shunted input and properly loaded output. 
Wrong. DC and cap coupled outputs shouldn't be measured loaded unless specifically instructed to do so, and very few are. The vast majority of inputs have some reference to ground at the input so shorting the inputs shouldn't make much difference. If open inputs produce excessive DC on the outputs, it's best to find that. 

To the OP,

Those numbers aren't bad. The fluctuations you're seeing aren't anything to be concerned about, especially since the amp wasn't really warmed up. I like to wait 2 hours before taking final bias and offset measurements. After 2 hours you can be sure a power amp is as warm as it's ever going to idle at and everything has reached thermal stability.