Time travel is the means by which humanity's descendants in the future attempt to change their situation by manipulating the past.
Mechanics[]
Time travel in the physical sense is not shown to be possible. The only thing that can travel to the past (and the future) is information. (S3E08: Archive) People in the future have developed a means of treating consciousness like computer data: consciousness transfer is a related technology that allows future people to "travel" into the past by uploading their consciousness into hosts who were historically about to die. These aptly-named "Travelers" then enact missions according to a Grand Plan to save humanity, to ensure a future with a ruined Earth and dwindling population does not come to pass. (S1E01: Travelers)
When Travelers arrive into the past, their actions create a future that already deviates from the one they left, be it major or minor changes. Successive Travelers come from this future, and they may arrive knowing what their earlier associates did for the rest of their lives. (S1E06: Helios-685, S2E07: 17 Minutes)
Travelers can only time travel to a point after the most recent Traveler because of "complicated reasons involving ripples in the timeline". (S1E11: Marcy, S2E07: 17 Minutes) Normally there are no do-overs, but this is more a problem of the amount of time elapsed between the future period and the target period in the past. The amplitude of space-time distortion is directly proportional to distance. 431 years in the future after 2018 (or year 2449) it is impossible to send a Traveler earlier than the most recent one, but sending a Traveler from 2018 back up to 20 years is doable and safe, provided a T.E.L.L., a consciousness transfer machine, and the requisite software and supercomputing hardware are also present. (S3E10: Protocol Omega)
Alternate timelines are known to exist side by side with each other, a lot of them with their own versions of Travelers also doing their thing. The Director exists in a domain outside of time, and from this vantage point it chooses which timelines to manipulate and which ones to discard. (S3E07: Trevor, S3E10: Protocol Omega) While time travel generally means going into an "alternate" timeline from the future a Traveler leaves behind, time travel from a present timeline into a concurrent one is also not shown to be possible. Historians can peer instead into these alternate timelines, called projections, if they neglect to take their stabilizing drugs after an Update. (S2E09: Update, S3E08: Archive, S3E10: Protocol Omega)
Major timeline changes can collapse alternate timelines and leave only a few or just one left. Trevor Holden notes that the Director must have declared Protocol Omega on millions of timelines after some irredeemable failure, and they happen to be living in one about to be destroyed by nuclear weapons. During the Protocol Alpha mission of retrieving the Fraser meteorite, several timelines are created as multiple Travelers download into the past. Most of the attempts fail, until a timeline is created where the Travelers succeed. It is not known for certain what happens to the timelines where the Travelers failed, although given Trevor's comments, they may also have been subjected to Protocol Omega. (S2E07: 17 Minutes)
Philip Pearson, after witnessing so many alternate timelines and impending nuclear apocalypse in his own, reports he's reduced to seeing only one last timeline where they must use Vincent Ingram's consciousness transfer machine to stop him from ever going back in the first place. Version One of the Traveler Program ends with Traveler 3468 preventing 001 from transferring into the past and warning qualified individuals about the existence of Helios-685 way earlier than expected. Further manipulations of the timeline and alternate versions thereof now spring from Version Two of the Traveler Program henceforth. (S3E10: Protocol Omega)