You mean the Lost Experience thing? We've learned quite a few things. I'll sblock them for the benefit of those who wish to remain unspoiled.
[sblock]
The Hanso Foundation is behind the Dharma Initiative, but they have publicly disowned it (there are still food drops coming from somewhere though).
TDI was created to prevent world destruction, by manipulating the input variables in something called the Valenzetti Equation, which is supposed to forecast when the human race is destroyed.
Alvar Hanso was instrumental in starting up TDI (although the idea seems to have come from Gerald and Karen deGroot), but he hasn't been seen for many years now. A man called Dr Thomas Mittelwerk (although he doesn't seem to actually have a doctorate) is running the show instead.
The Black Rock (the ship) was a slave trader, and owned by Alvar Hanso's ancestor, Magnus Hanso.
THF under Mittelwerk are working on some sort of genetic virus that will kill off "precise genetic targets", presumably people he believes would hasten the demise of the human race. They've done some pretty nasty things while researching this virus.
Both the Widmore Corporation (Desmond's ex's father's company) and Paik Heavy Industries (Sun's father's company) have strong ties to THF.
Mittelwerk has taken an interest in old shipping lines running out of Copenhagen. It is possible he is trying to figure out the location of the Dharma Initiative by locating where the Black Rock travelled.[/sblock]
I think those are the main plot points that are actually relevant to the Island.