This is a Thurible:
Actually, THAT one is not the norm. That's HUGE! (And most impressive - and kinda scary!) Most thuribles are small and are carried (and swung) by an acolyte, called a thurifer, and is used cense the altar, the Gospel book, the Eucharistic elements, and the people. At Saint Peter's we cense the altar, the Gospel book, and the Eucharistic elements at the 11:15 am service on all Sundays. Incense is only used at our other services on high holy days. Here's some more information about the thurible from The Catholic Encyclopedia.
A thurible is a "vessel suspended by chains, and used for burning incense at solemn Mass, Vespers, Benediction, processions, and other important offices of the Church... In its prevailing shape the censer consists of a cup, or bowl, which rests on a firm base and is provided with a hollow movable pan for holding ignited charcoal, a lid or covering, and four chains about three feet in length, three of which unite the bowl to a circular disc, while the fourth is used for raising the lid, to which one end is attached, the other passing through a hole in the disc and terminating in a small ring..."
Read the entire article in The Catholic Encyclopedia.