Morton's Fork is a logical dilemma in which people are faced with two equally bad options. You could think of it as being "between the devil and the deep blue sea," as the saying goes. Unless the victim of the dilemma manages to find an exception, the outcome of the situation will most probably be undesirable, as there can be no good outcome from any of the choices the victim is faced with. Many people find themselves struggling with Morton's Fork at some point in their lives.
This term is named after Lord Chancellor John Morton, who worked in England under Henry VII. According to Morton's logic, wealthy subjects of the Crown obviously had money to be spared for taxes, and poor subjects were clearly sitting on savings, so they could also bear high taxes. Rich and poor alike found themselves at the points of "Morton's Fork," paying high taxes.
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Like many logical dilemmas, Morton's Fork can have interesting implications. It sometimes comes up in game theory, with the game of bridge actually having a move called "Morton's Fork" after the dilemma which inspires it. Mathematicians and people who study human behavior are often interested to see how people respond to such dilemmas, and how they rationalize their behavior if the outcome turns out as poorly as expected.
When faced with two bad choices, the temptation may be to do nothing, but sometimes this is also a bad alternative. Sometimes, a more thoughtful consideration of the options either reveals an additional choice, or a choice in the array of existing options which is less repugnant. It may also be possible to subvert the dilemma by finding or creating an exception to the rule. Being between a rock and a hard place is sometimes solvable if one is willing to develop a hammer to smash the rock out of the way, in other words.
It can also be helpful to be aware of Morton's Fork when having arguments or discussions with people over whom one has some authority. If people feel cornered by bad options, they may lash out, a result which no one wants. Parents, employers, teachers, and others would be well-advised to think about the way they present options to their charges to assure them that there are choices to choose from, and that people are willing to work to make these choices as palatable as possible.