The pledge the statement refers is the Tennis Court Oath (1789).
The Tennis Court Oath happened when King Louis XVI didn't accept the Third Estate's demand for voting by head in the assembly of the Estates-General.
Louis XVI had called upon the Estates-General to deal with the economic crisis France was going through. In this assembly, each estate had one vote. The third estate, made up of the bourgeoisie, urban workers and peasants, didn't accept this inequality and demanded a vote by head.
When the king refused, the Third Estate left and broke into a Tennis Court nearby. There they took a collective oath "not to separate, and to reassemble wherever circumstances require until the constitution of the kingdom is established".