A false christ or false messiah is someone who wrongly claims to be God's chosen leader (the Christ or Messiah). Jesus warned about false messiahs in his teachings about the future, as recorded in Matthew 24:24 and Mark 13:22.
Jesus taught his followers about what would happen in the future. He told them that the temple in Jerusalem would be destroyed. He also warned them that they would face people who would try to trick them and treat them badly. He especially warned them about the difficult times that would come when the temple was destroyed. During this time, they should not believe people who falsely claimed to be the promised savior (Mark 13:21–23).
These false teachers would say things like "The Messiah is here!" or "The Messiah is there!" (Mark 13:21). They would even perform miraculous signs to try to fool God's chosen people. But Jesus helped prepare his followers by teaching them that before he returns as the divine Son of Man, there would be signs in the sky (Mark 13:24–25). When he does return, everyone will be able to see his power and glory.
From history, we know that Jesus’s teaching helped Christians to escape from Jerusalem before it was destroyed along with its temple in AD 70. His teaching also helped them avoid being fooled by people who falsely claimed to be the Messiah. Today, Christians continue to wait for Jesus to return in glory as the Son of Man.