In Aliens, at the beginning of the movie we see Ripley being discovered by a patrolling space craft. She is later revealed that she has been travelling for 57 years (correct me if I am wrong). Her daughter is already dead in her 60's, yet Ripley looks very young. How is that possible?
Space travelers in the Alien-'verse typically enter "Hypersleep Pods" in order to while away the journey time since even with fast FTL, spending months staring out of the window at the stars is pretty damned boring, likely to lead to self-destructive behaviour among the crew and would require a considerable amount of extra food and air.
Both the novelisation and the film's original script concur that the Nostromo crew open the film coming out of their hypersleep pods, the same pods that Ripley evidently entered at the end of the film (just after the credits rolled).
INT. HYPERSLEEP VAULT
Another lid pops open. A young woman sits up.
LAMBERT: What time is it.
Of them all, only Ash seemed relatively content. His only concern at the moment was for the mental condition of his shipmates. There were no true recreation facilities on the ship for them to turn to. The Nostromo was a tug, a working vessel, not a pleasure craft. When not performing necessary tasks her crew was supposed to be spending its blank time in the comforting womb of hypersleep. It was only natural that unoccupied wake time would make them nervous under the best of circumstances, and the present circumstances were something less than the best.
One of the central conceits is that hypersleep massively retards the aging process. A year in hypersleep is equivalent to centuries in realtime. At the end of Alien, Ripley enters one of these pods and enters a state of cryogenic suspension. This is how she is able to survive 50+ years without (much) visible aging.
According to the salvage team seen at the beginning of Aliens, the pods on the Nostromo are somewhat antiquated, even by the standards of the day, tying into the whole "space travel on the cheap" theme
From an out-of-universe perspective, placing the film so far ahead allows them to have her character age slightly without really having to go into a deeper explanation of why she's older in the sequel.
The Alien setting has FTL travel of varying speeds. People who travel on long journeys in slow ships travel in stasis, also known as cryosleep or hypersleep. These are the pods you see people enter or exit near the beginning or end of most of the films.
The point of stasis is to reduce the consumption of resources and slow down aging. Effectively, people who do a lot of deep space travel have a biological age significantly lower than their chronological age.
1The capsule looked too simple though for a cryosleep type.– eYeMay 19, 2016 at 12:48
1They have FTL travel in the Alien Universe. Depending on how modern/expensive your ship is, it can be pretty darned fast– user7812May 19, 2016 at 12:50
2@eye That's a matter of opinion. Regardless of how simple or complex the prop is, the technology exists.– T.J.L.May 19, 2016 at 12:50
1'Cause cryosleep, yo. Plus one. Don't need no screen shots, scripts, or videos.– MazuraMay 19, 2016 at 23:39
Ripley was asleep for however long she was asleep. The idea is more to do with time differences in reference to where she is in space versus time passing, back on Earth. Einstein proposed that if someone where to travel away from Earth at great speed and then return to Earth sometime later, Earth time would have moved much more quickly than the space travellers time.