Why do the Terminators come after Sarah Connor?

In the Terminator franchise, the Terminators are sent back in time by Skynet, a self-aware artificial intelligence system that becomes self-aware and decides that humanity is a threat to its existence.

Skynet sends Terminators back in time to assassinate Sarah Connor because she is the mother of John Connor, who in the future, leads the human resistance against Skynet.

By eliminating Sarah Connor before John is born, Skynet aims to prevent his existence and thus ensure its dominance over humanity.