What does a Summer/Winter switch on furnace air ducts do?
I assume you are in a cold climate, like Minnesota (where I am).  I will address your question in three parts; the first two have to do with the humidifier.


The "winter" setting on the duct in your photo:  It appears from the photo that the duct in question goes from your humidifier around to the return (intake) side of your furnace's ducting.  This needs to be open in the winter to allow the humidifier to function, but closed in summer.  If you leave it closed in winter, then your humidifier will have almost no effect.  If you leave it open in summer, then your A/C's efficiency will be reduced.
The white control box in your photo is the controller for the humidifier.  On mine, the knob settings are "off" and 1-7 (1=less humidity added to your house, 7=max humidity added).  There is also a "test" setting past 7 that will turn on the water.  Someone appears to have labeled yours with a "W" to indicate what they think is the best winter setting.  If you leave this "off" in the winter, then your house may become uncomfortably dry.  It should be set to "off" in the summer.  There are no fans or other moving parts in your type of humidifier; there is a water valve that is either closed or open (the humidifier is on when water is running through it). 
If you have other ducts in your house that are labelled "winter," then those are probably just changing which rooms get the most air blown in.  In my experience, people like to direct more heat into lower levels (e.g. basement) in the winter. (edit: Evil's response on this point is more complete).