200 years after Ellen Ripley dies in Alien 3, the military essentially mucks out the acid pit in which she died, extracts DNA and clones her. They do this because they were aware that she had a queen alien inside of her, which they want to use to make new aliens, advance science, etc. Along for this ride is a team of space thugs who bring the military the cargo they need to produce new aliens - fresh, live humans.
Some of the unsuccessful Ripley clones
Alien: Resurrection of course pales in comparison to the first and second movie, and while much of this seems like a desperate attempt to cash in on the fan base from the first two films, there are some parts that help move the narrative along. Example: once Ripley is cloned, some of her new genetic make-up is combined with the alien dna, thus making her a 90/10 human/alien badass. Her ability to use her own blood as acid comes in handy a few times.
Also, Ripley starts to feel an affinity for the creatures which she spent so much of the first three films trying to destroy. This new, care-free, alien-loving, hard-core Ripley is refreshing and presents some actual intriguing conflicts towards the end of the film with a new alien that is uniquely terrifying. So, although not worthy of its predecessors, not bad if taken out of the Alien saga context.