You'll usually hear this expression in the form of a rhetorical question: "Does a bear sh*t in the woods?". Sh*t is of course a fairly common word that means waste matter excreted from the bowels. Woods are forested areas, which is where you will often find bears (and therefore where they would normally defecate). That means the obvious answer to the question is: "Yes, of course". However the question is usually used rhetorically to make a point rather than expecting an answer. For example, if someone were to ask "Do you want another drink?", he might get the answer "Does a bear sh*t in the woods?" meaning "Yes, of course I want another drink". The other rhetorical question that you might hear used in this way is :"Is the pope catholic?". It's used in the same way as "Does a bear sh*t in the woods?" to mean "Yes. of course". Hope this helps.

Adding on to Gareth's answer - "Does a bear _____ in the woods?" Is a way of saying "yes," when the answer is obviously "yes." So, if it was a hot hot day and you had been exercising hard and you are panting and sweating so that it would be obvious to any person that you wanted a drink. And someone asked "Would you like something to drink?" You could answer "Does a bear s*** in the woods?" Because of course you would like something to drink. "Is the Pope Catholic?" is another way of saying "yes, obviously." And sometimes people mix the two questions up and say "Does the Pope s*** in the woods?" - Again that means "Yes."

This is a fairly crude or basic expression, a little like "Is the Pope Catholic?" in meaning. Where else would a bear perform this function? In fact I have no idea about the habits of bears. But the point is that this expression is used to suggest that something is obviously and clearly true. Do I like burgers? Is the Pope Catholic? Does a bear ...? See https://www.urbandictionary.com/define.php?term=Does%20a%20bear%20shit%20in%20the%20woods%3F