The famous "when will you wear wigs?" exchange comes from a 2004 prank interview in which Lord of the Rings co-star Dominic Monaghan interviewed Elijah Wood while Wood did not realize who was asking the questions.
Why people search this
The meme is old enough that many people remember the phrase but not the interviewer, the show, or the context.
Why it became funny
The questions sound both simple and surreal: "Do you wear wigs?" "Have you worn wigs?" "Will you wear wigs?" The repetition turns a normal celebrity interview into absurd comedy.
Bottom line
Dominic Monaghan interviewed Elijah Wood about wigs. The clip still circulates because Wood's confused patience makes the odd little sequence funnier every time it repeats.