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. 
That DMM is showing a couple of different things.   First, with an open input you are probably picking up some 60 Hz noise.   Try shorting the input and see if the fluctuation changes and DC offset settles down to either a positive or negative number.   Capacitive coupled outputs have a bleed resistor to ground to shunt the initial charge current to ground.   Depending on the cap, it can take quite some time for the leakage to drop to zero.   Any polymer cap, that is polyester, polypropylene, etc., will have zero leakage but will have a charging current that should dissipate in a short time.  Electrolytics charging current and leakage current is much the same since their leakage is also the dielectric stabilizing under a charge.   Consequently, they can have leakage current that can last for many hours.  I have measured leakage in good quality electrolytics that took over 24 hours to subside.   The cheap ones can take several days.   Do understand you can also have an electrolytic coupling at the input as well as the output, which will get amplified and appear at the output.  In general though, the numbers you are reading are nothing to worry about.
The numbers sound fine.

Unless it's a tube amp. That would be a weird one.
I like the DC Offset to be under 10mV but depending on the specs that might be nominal.