The Time Variance Authority is in charge of maintaining the Sacred Timeline to keep the multiverse from exploding. Their dogma states that a multiverse leads to multiversal war and the end of everything, so they're supposed to protect the Sacred Timeline from branching out to keep that from happening. A Nexus Event is something that causes a splinter from the Sacred Timeline. If a Nexus Event goes past something called the Red Line, that means there's no stopping that branch. The steeper the spike, the faster they need to get in, find the variant who stepped off the Sacred Timeline, take them out, and reset that branch of the timeline. The Variant goes through a series of bureaucratic bullshit until they're in front a judge, and all Variants are always found guilty. They are pruned, or deleted. What really happens is that everything from that splinter of a timeline gets moved to the end of the time, in a void where a creature that feeds on matter and energy consumes everything the TVA dumps there.