A Sario Rip is a rift in the fabric of space-time, caused by a massive, precise explosion. It can send those in the vicinity of the explosion either forward or backwards through time.
If a being is taken backwards in time by the Sario Rip effect, they must reverse the effect before the date and time that it originally occurred, as one being cannot exist simultaneously in more than one location. Prior to the time of the rip, they are protected by the 'backlash' of the rip effect, but if they fail to reverse the effect before the original event took place, they will cease to exist in all timeframes.
Animorphs' encounters with the effect
The Animorphs experienced the Sario Rip effect twice. In their first encounter with the phenomenon, they were sent roughly 24 hours back in time when the Dracon beams from the Blade ship and a experimental Bug fighter they had stolen collided and they crash-landed in the Amazon rainforest. While trying to escape Visser Three and the Yeerks, who had also been sent back in time, Jake was able to undo the Sario Rip effect when he was killed by Visser Three. Because another Jake was still alive in another location, his consciousness merged with his other self, allowing him to prevent the event that caused the rip.
A few months later, the Animorphs investigated a nuclear submarine that had gotten lost in the ocean, in the hope of rescuing its crew. The submarine accidentally detonated one of its warheads, which triggered another Sario Rip and sent them to the distant past - into the Cretaceous period. Although the Animorphs tried to undo the rip by stealing a nuclear bomb from an alien race called the Nesk (who were attempting to colonize Earth in the past), the rip was eventually reversed when a massive comet struck the Earth, triggering the end of the dinosaurs and sending the Animorphs back to the future. 
Interaction with Morphing technology
Main: Unusable Morphs
The first rip's effect were completely negated, and thus Jake found that the jaguar and spider monkey morphs he acquired did not work, as the timeline, in which he and the others acquired them no longer existed. However, although no such negation occurred with the second rip (which was simply reversed, leaving the timeline intact), the Animorphs discovered that an unspecified side-effect of the Sario Rip prevented them from using their acquired dinosaur morphs in their own time.