Etymology

French, literally nobility obliges

According to the French Wiktionary, the Dictionnaire de l’Académie française defines it thusly:

1. Whoever claims to be noble must conduct himself nobly.

2. (Figuratively) One must act in a fashion that conformes with one's position, and with the reputation that one has earned.

Noun

noblesse oblige

1. the honourable obligation that is the responsibility of those of high rank; in American English this often includes the expectation of benevolent actions such as helping those less fortunate.

The Oxford English Dictionary says that the term "suggests noble ancestry constrains to honourable behavior; privilege entails to responsibility." Being a noble meant that you had responsibilities to lead, manage, etc. You were not to simply spend your time in idle pursuits.