The word "smear" generally means to spread or apply a substance over a surface in a messy or careless way. It can also refer to making a false accusation or damaging someone's reputation through dishonest portrayal. In both contexts, it indicates an action that obscures or casts a negative light on something.
The word "smear" originates from the Old English "smyrgan," which means "to smear, to spread," and is related to similar words in other Germanic languages.