Wikipedia tells us:
A novena is a devotion consisting of prayer said (most typically) on nine successive days, asking to obtain special graces. These may consist of small prayer books, recitation of the Rosary, or small prayers through the day. There are four recognized categories of Novenae, those of mourning, preparation, prayer, and those which are indulgenced, however, a given novena can belong to more than one of these categories.
The practice of saying novenas is derived from Scripture. After Jesus' Ascension into heaven, he told his disciples to pray together in the upper room and devote themselves to constant prayer (Acts 1:14). The Apostles, Blessed Virgin Mary, and other followers of Jesus prayed together for nine consecutive days, concluding in the descent of the Holy Spirit on Pentecost.
Here is an example: