I've done some looking into this via web search (and reading trustworthy sites), and I think I might have an answer to this, though I want to see what you think about it (since you are an atmospheric scientist who works for NOAA, who has completed significant graduate-level work in meteorology, and who has authored or co-authored dozens of publications in this field, while I am merely a weather enthusiast who has read a few things from time to time).  

Basically, from what I read, I think that internal variability is based on how the weather is fundamentally chaotic: It is impossible to get exact and precise weather measurements for every area on Earth at every second, so it is impossible to make absolutely accurate forecasts, let alone even fairly accurate ones for more than a few days in advance. 

According to what I read, because measurements have improved over the past few decades, forecasts are pretty accurate for up to a week in advance (and are sort of accurate for a few weeks in advance), plus measuring tools are continuing to improve (which means that weather forecast accuracy is probably going to continue going up for a while). 

Even so, because of internal variability, it is impossible to say what the exact high temperature or low temperature will be tomorrow, let alone say with absolute certainty whether or not it will rain or snow.  The best you can do is give a probability of what it is expected to be.  

So, is this what internal variability is?