The monastery was founded by William I of Acquitaine, and enjoyed the benefit of series of very long lived, saint-abbots (Pope Benedict XVI spoke about one of them in his last General Audience). It served as a force for reform both of monasticism (at its height the Cluniac Congregation included 825 monasteries, all directly dependent on the mother house), and the Church and society more generally. It was a particularly important support base for the reforms of Pope Gregory VII.
Cluniac monasticism stressed the moderation of St Benedict's Rule rather than ascetic extremes (though the Cistericans twelfth century critique of Cluny is clearly vastly exaggerated) - and its most well known feature was its strong liturgical focus. Central to its raison d'etre was the new emphasis in the earlier middle ages on the importance of the intercessory prayer of monks.
The Monastery itself became enormously wealthy - it accumulated perhaps the largest library in the West, and its Church was certainly the largest until the construction of the new St Peter's in the sixteenth century.