To smear something is to smudge or blur it. You might literally smear your pen-and-ink drawing, or figuratively have your reputation smeared by getting caught in a lie.
You can also smear things physically by smoothing them onto another surface, like when you smear lip balm on your mouth or smear cream cheese on your bagel. When you smear a person, however, you cause them real harm by hurting their reputation badly. A politician might smear an opponent by falsely claiming they lied about where they went to college, for example. That kind of smear can be hard to erase.