Lost unravels mysteries about the characters and the island in layers, which means that even those of us who have seen every episode don't know why certain things happen. Mysteries are revealed bit by bit. Many character mysteries are revealed through flashbacks and flash forwards. In most episodes, there are flashbacks scattered throughout that give insight to a specific character's life before the plane crash.
There is some kind of monster that is made of smoke on the island, but the survivors don't know what it is.
At one point, survivors build a raft and four people, including one ten-year-old boy, sail away, hoping to get rescued. Instead, a band of pirates steal the boy and blow up the raft. The other survivors stay on the raft wreckage, which takes them to shore on the other side of the same island where they'd crashed. There, they find survivors who had been in the tail section of Flight 815.
On the island, Locke and Boone find a hatch. Locke is obsessed with getting into the hatch, led by visions. In their quest to get into the hatch, Boone dies from injuries sustained by falling off a cliff in a small plane they'd found on the island.
With dynamite found on the island, they are able to get into the hatch, where they find Desmond, who has been living in there, punching numbers into a computer every 108 minutes. Desmond runs off and Locke sets up a schedule of shifts to make sure the button gets pushed, though no one knows why it has to be done. When Desmond returns, he figures out that the one day he didn't push the button in time was the day Flight 815 crashed on the island. Locke loses faith in the hatch and forces the others to stop pushing the button. The hatch blows up.
A war breaks out between the crash survivors and the Others, resulting in almost all of the Others being killed.
The numbers 4 8 15 16 23 42 are very significant to the show.
Also, many characters show up in other character's flashbacks.
A French Woman lives on the island and has been there 16 years, since her research boat ran aground. The others from her group have all died. She tells the plane survivors of The Others who live on the island. They are the ones who have taken the boy off the raft, and they eventually get control of three of the survivors.
Jack, Kate, Aaron, Sun, Sayid, Hurley, Desmond, and Frank make it off the island, but lie about where they have been. After talking to Ben and seeing Locke dead, Jack decides to get everyone to go back to the island.
They return back to the island with some of them in 1977 and some of them in 2007.
Jacob is the leader of the island, though no one but the Other, Richard, seems to be able to see him, until Locke and Ben go to see him and Locke convinces Ben to kill Jacob. Locke is dead, however, so it appears that someone has taken over his body.
Jack drops a bomb into the Swan hatch possibly killing himself, Kate, Juliet, Sawyer, and the others who were around them. But they don't die, instead they are zapped back to the present, but they are still on the island. Frank, Miles, Richard, Sawyer, Kate, and Claire get off the island on an Ajira plane. Hurley, Ben, and Jack stay on the island, but Jack dies from injuries sustained from the Man in Black (masquerading as John Locke) and from going into the light cave and replacing the cork Desmond had taken out.
Hurley sends Ben to close up Dharma stations and fetch Walt and the three of them continue to live on the island.