How did the outbreak of plague in the 14th century contribute to the decline of feudalism in Europe?

Through much of the Middle Ages, serfs were not allowed to move off the manors where they lived. For the most part, they had to live and work in the places where they were born.

The plague reduced the rural population so much that many members of the nobility did not have enough serfs to work their land. In fact some manors were abandoned altogether, because there were no serfs to work on them. The result was that a number of nobles bribed serfs to move illegally to their manors, and protected them once they got there. This broke the old manorial ties.

You should understand, however, that the manorial system was never in use over all of Europe, and it was already on the decline long before the plague. Also, in some places, it lasted until long after the Black Death was over. In some places, it was still in place until the 19th century.