Note: I didn't use much info from everyone else, i used some and made my own idea of what could of happened. Please remember that he is deleted from Minecraft now, so don't say "but he's not real anymore" or anything like that.
Theory:
When Mojang created Minecraft, They tried making a Steve skin for classic version, but failed trying and accidentally forgot the pupils, so later on they made a new Steve skin so the other skin was thrown in the recycling bin.
During Alpha, a user played Minecraft and found a copy of Steve's skin, but with no pupils in the fog. The user posted this on the Minecraft forum with a picture that looked like this (I only have a link because it doesn't let me put in the picture by itself)
http://2.bp.blogspot.com/-H56Ko-9fB0M/TZJn3mrXJFI/AAAAAAAAACg/aI0bXT4Wfuk/s1600/Minecraft%2BHerobrine.jpgThe forum topic was deleted five minutes later, he tried looking at Herobrine's skin, but the page had a 404.
He contacted Notch, and Notch said, "He did, but he is no longer with us." Which either means that was when he said that he chucked it in the recycling bin, or, a virus occurred so his ghost still lives in the game.
Other people had sightings of Herobrine after that user found Herobrine in the first place. Herobrine can morph into animals (with no pupils), turn into a chicken and go underground, put small sand pyramids on water, and etc.
I had a thought that Herobrine has three forms, 1. Miner: Usually goes in caves, breaks blocks of anykind, can destroy bedrock.
2. Stalker: Usually stays in fog, Stalks player, Builds things like pyramids on water, and creates signs that says "Stop!"
3. God:Can be summoned, can walk in front of you anytime it wants, burns you up, cannot be killed.
Ever since Minecraft Beta 1.6, Notch said in the update news thing, "Herobrine Removed." Which was never true.
On Minecraft Beta 1.8, Endermen were created. Endermen must have killed herobrine, however, Herobrine's soul lives in all of the Endermen.
Another thing is that Herobrine was probably the
REAL Steve, but Notch decided to make prototypes of Steve going all over the place minecraft, mining, eating, farming, and all of those stuff.
As long as there is mankind, there will always be war
~Some Person