Both the Eladrin and Wilden have Fey Origin, which means that the characters ancestors were native to the Feywild, so the character is considered a fey creature for the purpose of effects that relate to creature origin.
What are these effects?
There are items that have powers and properties that look for fey origin:
I can't think of any feats that require "fey" but I could imagine such.
I can't think of any monsters that have powers (or class powers) that look for fey, but again I could imagine such.
Mechanically these effects are (so far) defined as above, but consider the LFR example Bryant is using: 'the purpose of effects that relate to creature origin.' is a design space that is completely open to the DM.
"Fey" could be used as a handle for providing a bonus or access on adventures or campaign details. Since AD&D, I've written scores of dungeons with feature-rooms or NPCs or items that say "those with elven blood may get a bonus to decipher these writings.." or "only those with orcish blood may approach the altar.."- if you have some fey and some non-fey in the group and want to create kind of a flavorful area (for example, a Feywild passage that effects characters differently).. this is a good way to do it.
These origins (not just fey, but living construct (warforged), undead (revenant and dhampyr), immortal (deva), goblinoid, etc..make great handles for things.