To smear someone is to use false information or accusations to harm their reputation.
A smear campaign in politics is repeated uses of smears in an attempt to try to damage someone’s reputation, typically to make them lose an election.
Psychology Today says that smear tactics work: “Assuming that acceptance of these slurs is related to voting choice, this suggests that in some cases, political slandering works. And not only that, it works on the group that is perhaps most important in swinging an election: politically undecided individuals. We may report hating these slanderous statements. But, it appears that they might make up our minds for us when we haven’t already.”