Burning incense is one way to adjust the smells and atmosphere of your home.
Incenses are like candles where they can be used to give a more pleasant scent to houses or to get rid of a specific and unpleasant smell, usually by covering it. Scents can be a powerful emotional trigger.
Incense can also be part of home rituals -- for instance religious rituals involving burning incense at a home shrine. Many parts of religious and Asian culture as a way of worship or mourning.
Incense is heavily used in Asian culture.
Incense is associated with some health issues. Like other smoke, breathing incense may cause respiratory problems and has been linked with respiratory cancers. Candles, incense and other things can contribute to indoor pollution. The risks can probably be reduced by making sure you have adequate ventilation.