Definitions
1.nounA blemish or smear, especially a dark or sooty one."There was a smudge on the paper."
2.nounDense smoke, such as that used for fumigation.
3.nounA 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.
4.noun(especially in the phrase "smudge stick" = "stick of incense") A quantity of herbs used in suffumigation.