Something came off of my window, can someone help identify what it is?

What is the measurement of that piece? and of your windows?

This piece, having come partially detached, would have been the cause of the window binding. It's function will likely be to prevent air exchange between outside and in (if the window now still has resistance against a fast drop comparable to you other windows, the piece will definitely be draft prevention). Depending on your local climate, you may suffer some minimal increase in heating/cooling costs, but that's likely to be your only concern. You could light a candle or something else that produces smoke and determine if this window has more air disturbance than another similar window. Depending on the particular design of your windows, you might be able to remove the lower sliding half by lifting it up a foot or so, then pushing it over to one side (don't use a lever, just your hands). That would allow you to replace the strip. If you can't do that and if you are concerned re drafts, then you can call in a window company. But that will cost you and may not be worth the expense.