What is it for ? It gives information on the contents of the disc, in Japanese. Many discs (especially from the LP days) have very little info on their cover, the obi comes to guide the buyer.
Why is it sometimes missing ? The obi was not originally made to be kept, it is info that can be discarded once the purchase is made. Many consumers throw them away. Its' value is only aesthetic (not always) and to the collectors.
Is there always an obi with a new, sealed Japanese disc ? Contrary to common belief, answer is no. On LDs, some manufacturers cut their cost by printing the necessary info on the jacket, or by putting a sticker on the wrap, resulting in discs without any obi. Those i have confirmed to proceed this way are Toho, Nikkatsu, Bandai, Embassy, PolyGram, Nippon Phonogram, BMG and VideoArts, but not necessarily on their whole catalog.
The obi is discarded by some, but for many buyers it has a value, and for completist collectors it is absolutely necessary to have it with an item. That puts upward pressure on the price of those discs that have the obi, and the spread with those without may get wide if the obi is rare.
Example of a LaserDisc with and without obi:
The Star Wars "Making of a Saga" came with a blue obi. Check the pictures below to see how the jacket looks with or without the obi on:
Without the obi:
Personally, i think the disc looks better without. Many original buyers thought the same and tossed away the obi, resulting in that today, only half the copies found on the used market come with it.
However, if you come across the Classic Creatures LD as well, then you start to appreciate the fact that the two discs share a common design for their obi, making them really look like a pair, and in that sense the obi is definitively a plus:
Example of a LaserDisc with no obi:
Thin Lizzy "Live and Dangerous" was released by Nippon Phonogram without obi, instead there was a round sticker on the wrap:
Thank you for reading these lines.
Nicolas