It borrows from the storyline "Days of the Future Past" and introduces new characters such as Apocalypse (voiced by Liam Neeson), Cable (Stephen Lang), and Omega Red (Mickey Rourke). There is alot going on and reading the plot summary should clarify some things. Enjoy.
After the events of X2, humans and mutants have made a truce and learned to co-exist. However, a mutant known as Apocalypse has re-ignited the war between both sides by invading different regions of the world and the government responds by putting "Project: Wide Awake" into motion and deploying Mutant Capture Units also known as Sentinels. Magneto sees this as an opportunity to build an army and fight against them. Among Magneto's army is Arkady Rossovich (Omega Red), a mutant looking for revenge against the X-Men for putting him in prison. Apocalypse banishes Wolverine into the future for trying to stop his plan and promises Cyclops he can bring Jean back if joins his crusade.
In the future, the world is over run by Sentinels and small pockets of resistance are lead by a mutant known as Cable. Wolverine crosses paths with them and Cable assures him he can send him back to his time if he helps the resistance find a way to destroy the Sentinels.