The events on the Island throughout the 6 series all happened. The Island had mystical powers (never fully explained)and was protected by Jacob whose twin had died and become evil.
The passengers were brought to the island by the powers of Jacob to seek a replacement protector. They all had flawed lives.
Some survivors died on the Island over time. (Charlie, Sun and Jin and others)
Some survivors left the island and then came back to help those left behind. (Jack, Kate, Hurley, Sayid, Sun.)
Some survivors escaped the island again in the final episode and presumably got on with their lives to die naturally at various stages through their lives.(Kate, Sawyer, Clare)
Jack volunteered to replace Jacob and sacrificed himself to protect the Island culminating in an ultimate battle with the evil force on the island (black smoke manifesting itself as Locke).
Hurley stayed on the island after Jack died and became it's protector with Ben as his right hand man.
The final series showed a supposed alternative timeline where the original plane landed safely and the passengers appeared to be getting on with their lives. They all kept coming across each other in this timeline (often helped by Desmond) and some of them started to recognise each other.
It became apparent that this alternative timeline was actually purgatory and was created by the passengers to help them right their wrongs and find peace before moving onto heaven.
They all died at different stages of their lives but once all were content and at peace they were reunited at a concert and then gathered in church with Christian (Jack's Dad). This was them moving from purgatory to heaven.
Sorry - have gone on for yonks!!