A paradigm is a framework of rules and theories that follow a distinct pattern (the word paradigm actually comes from the Greek word for pattern). Throughout history, paradigms have changed in events referred to as paradigm shifts. An example of a paradigm shift would be the promotion by Galileo of a heliocentric solar system, versus the common paradigm of a geocentric solar system. Paradigm shifts are often met with resistance, as many become stuck in paradigm paralysis. In this case, the Roman Catholic church condemned Galileo's findings and forced him to recant.
MSN's Encarta defines a paradigm shift as "a radical change in somebody's basic assumptions about or approach to something.". The term paradigm shift was introduced by Thomas Kuhn in his 1962 book The Structure of Scientific Revolutions. The Stanford Encyclopedia of Philosophy wrote the following regarding Kuhn's concept of the paradigm shift:
"A mature science, according to Kuhn, experiences alternating phases of normal science and revolutions. In normal science the key theories, instruments, values and metaphysical assumptions that comprise the disciplinary matrix are kept fixed, permitting the cumulative generation of puzzle-solutions, whereas in a scientific revolution the disciplinary matrix undergoes revision, in order to permit the solution of the more serious anomalous puzzles that disturbed the preceding period of normal science." 
Kuhn had a theory about the history of science which denied the existence of scientific progress, and which denied the rationality of scientists switching from one theory to another. He popularized the term "paradigm shift" to describe such a switch.
A paradigm paralysis occurs when individuals refuse to accept a paradigm shift. Often, this can have devastating results, especially in the business world. A famous example is the rise of the quartz movement wristwatch. In 1967, Swiss watchmakers displayed the first model of a quartz movement watch. Despite being more accurate, cheaper, and less intricate than their mechanical counterparts, the Swiss refused to change their method of watchmaking. In 1969, the Japanese company Seiko released the first commercially available quartz movement watch. The watch proved popular enough that as of 2010, nearly 95% of all watches use quartz movement in the design. The Swiss' failure to adopt to the new paradigm of quartz movement instead of mechanical movement devastated the watch industry of Switzerland.