noun

• (US) A heap of damp combustibles partially ignited and burning slowly, placed on the windward side of a house, tent, etc. to keep off mosquitoes or other insects.
  "Then "smudges" are in vogue,—heaps of damp combustibles placed on the windward side of the house and partially ignited, that their inky steams may smother the mosquitoes while we take our chance. I have had a "smudge" made in a chafing-dish at my bedside, after a serious deliberation between choking and being devoured at small mouthfuls; and I conscientiously recommend choking, or running the risk of it, at least."
• (paganism, especially in the phrase "smudge stick" = "stick of incense") A quantity of herbs used in suffumigation.
  "Devil's dirt or asafetida ground together with fenugreek and black cumin seed is used as a smudge against witches and […]"

verb

• (paganism, intransitive) To burn herbs as a cleansing ritual (suffumigation).
• (paganism, transitive) To subject to ritual burning of herbs (suffumigation, smudging).
  "This is easily done using incense to smudge yourself or taking a cleansing bath. To smudge your body use an incense mixture such as sandalwood, lavender, frankincense or myrrh."