This word does not mean some sort of Islamic clothing. Nor does it mean an awkward toupee. Those were among two of my guesses when I was trying to figure out what this odd word might define. None of my guesses were even close.
According to Wikipedia:
The Birkin bag is a handmade purse by Hermès and named after actress and singer Jane Birkin. The bag is a symbol of wealth due to its high price and elusiveness to the public.[1]
Its prices range from $9,000 to $150,000. Costs escalate according to the type of materials. The bags are distributed to Hermès boutiques on unpredictable schedules and in limited quantities, creating scarcity and, intended or unintended, exclusivity.