Shimano Thumb Shifter button question
It's a knob that allows you to switch the shifter between SIS mode and friction mode. I discovered that here where they have images of the user manual for this shifter or a similar one:



SIS stands for Shimano Indexed Shifting, which is the type of shifting most riders of newer bikes are familiar with - clicking between gears by number. Friction shifting means the lever moves smoothly and you learn to find the correct gear by feel. If you've ever ridden an older road bike (the kind that often has downtube shifters), you've probably experienced those. 

As always, Sheldon has more info.