What is the actual size of a 26x1.5/2.2 tube? I've got some spare Specialized "Airlock" inner tubes that are size 26x1.5/2.2. That means 26 inch rims, but what does the 1.5/2.2 mean? It fits 1.5 to 2.2 width tires or something else? Curious what this kind of size specification means.

Secondly, will it be advisable to use it on my bike that has 26x2.1 tires?
Tubes expand quite a lot as they are inflated - Try pumping one up on its own and see how quickly if expands (don't over do it unless you never want to use the tube again.). The way tubes and tires work, the tube holds the air in, the tire prevents the tube expanding.  

The 1.5-2.2 means the tube is suitable for a tire 1.5 up to 2.2 and is ideal for you 2.1 tire.