What happens to Master Chief at the end of Halo 3?

I just finished Halo 3. Towards the end, you see Master Chief sit down, and a bright light surrounds him. His last words are, "We'll make it".

What happened to him? Did he die?

Well according to the Halo Novels that I've read, He is taken into a Dyson sphere, which is a really small sphere, but inside it using slip-space technology (halo equivalent of hyperspace) there can be a world of any size that is in a slower time, and can be like that infinitely with more and more spheres inside. (sort of like Inception, but instead of time being fastest in lower levels, it's slowest in real-time and increasingly slower. but it is an inverted sphere.

In Halo 4 he returns from it though, and is once again the character you play as in campaign, although they are training the spartan-4s. (Spartans=ancient Greeks, spartan-2s = master chief and the other 74 spartan-2s although only about 40-50 survived the physical augmentations, spartan-3s had 2 batches, 1st one had 300, at age 12 they were sent to attack a base, they won, but only 2 survived, 2nd batch, forerunner machines kill all but ten, 5 of who are put in really deep dyson spheres, and mortally wounded. spartan-4s don't know much about, but the multiplayer in halo 4 is supposedly their training to give more sense(didn't make sense why Spartans and elites were on teams together and switched teams every match, and Spartans fought Spartans, now it does because it all trainee Spartans versus each other in whatever their "trainers" decide (aka custom games host, or random team selection in matchmaking)).

After he says that, the front half of the Forward unto Dawn (with the Arbiter piloting) jumps to Earth, and the back half, along with Master Chief and Cortana, appears to jump to some other location in space. The people on Earth believe Master Chief to be dead, but he survives and goes into cryo-sleep. The final shot of the ending shows that the half of the ship with Master Chief is near/heading towards an unknown planet.

This video shows the ending, starting from the point after he says "We'll make it" and there is a bright flash

More recent information released about Halo 4 reveals that

At some point after these events, Master Chief is awoken from cryo-sleep and they land on the planet. There, he confronts previously unseen creatures and Covenant.