Smudging is a ritual purification by smoke, common to most of the indigenous peoples of the Americas. It has been widely adopted by many non-natives.
All ancient cultures burned things of various types for spiritual reasons. Incense is thought to 'please the gods' with its scent, and resins such as frankincense and myrrh are considered suitable gifts. Native Americans use various herbs that are thought to purify a person, place or thing by virtue of the interaction of the smoke with the item. A space in which a ritual is to take place is smudged with smoke, as are all the ritual instruments and the people who pass into the space.
Herbs used in smudging are typically sages, cedar or sweetgrass. Central and South American tribes also use copal, resin from a variety of different trees, which has a pleasantly sweet scent when burned. Herbs are typically tied up in hand-sized bundles called smudge sticks to dry. Sweetgrass, a tall plains grass with a sweet vanilla scent, is braided into 'whips'.
In a ritual purification, the smudge stick is lit at a flame. After a few moments, the flame is blown out and the herb continues to smolder, releasing quantities of smoke into the air. If a space is to be purified, the smudge stick is carried throughout all parts of the space; if necessary, smoke can be directed into corners with a feather fan. Smudging an object just entails passing the object through the smoke several times. People can be smudged by fanning the smoke over their bodies as they stand.
Sage is believed to drive negative influences away, surely a wise precaution to take before interacting with the supernatural; sweetgrass is said to attract good spirits and energies, so typically sage is burned before sweetgrass. Natives of the Pacific Northwest use cedar for both purposes, expelling negativity and attracting positive forces. Smudging with cedar is sometimes called 'cedaring'.
Many people of all cultures now enjoy smudging. If they feel 'bad vibes' in their home or about an item, smudging it, they claim, will dispel the negative energies. Are they right? Who can say? Still, if you find yourself arguing with your family over insignificant things, or buy something at a yardsale that, once home, gives you the creeps, try smudging your home or the item. It may not help, but it certainly can't hurt.