Classifying every particular case as an example of one of two extremes when in fact there is a range of possible positions that can be occupied within the extremes. This is a variety of false dichotomy (eg, 'I know some christians that are such hypocrites, so I reject christianity entirely'. eg, 'some parts of the bible are ambigious and open to different interpretations, therefore all of the bible must be this way'). Black-and-white thinking occurs when you try to make the world fit very simple preconceived categories.
For instance, to ignore the fact that there are many position between being completely insane and being sane, treating everyone as if they must be simply one or the other would be an instance of black-and-white thinking. Someone who treated insanity as an all or nothing phenomenon would be seriously distorting the facts. There is a continuum along which all of us find ourselves (although our position on this continuum is by no means fixed for all our lives.) Similarly, to say everyone is either a teeetotaller or else an alcoholic would be to set up another obvious false dichotomy based on black-and-white thinking.
This is not to say that black-and-white thinking is always inappropriate: in some cases there really are just two positions which can be adopted. For instance, it would not be unreasonable to treat all responses given in a multiple choice mathematics test as either correct or incorrect; nor would it be inappropriate to divide runners into those who have run a mile in less than four minutes, and those who haven't. In both these examples there are not any positions which can be occupied between the two extremes. However, in cases where intermediate positions do exist, black-and-white thinking is always an oversimplification. Sometimes it is more than this: it can be used as a form of rhetoric, as for example in the cliche, 'If you're not for us, you must be against us', which sets up a false dichotomy of the black/white kind, ignoring the possibility of neutrality and of degrees of commitment in order to persuade the listener to take the plunge and support the cause in question (eg, 'either you are a JW and will survive Armageddon, or you are not and will be destroyed.' eg, 'If you are aware the Society have made wrong date predictions, then you must accept that they are false prophets, therefore you must leave the Organisation or you are also a false prophet and nothing but a hypocrite in God's eyes'.)