Keeps predators out. The octopus can get through pretty much any opening that its beak (the only hard part of its body, other than the lenses of the eyes). The one in the .gif is tasting the tip of the finger (an octopus has taste receptors in the suckers), and they are extremely curious.
When SCUBA divers do beach cleanups we are told that a bottle or can on the bottom for more than a few weeks is probably no longer trash - it's habitat.
(And, to be a bit of a pedant, an octopus doesn't have any tentacles, in the modern usage of the word based on structure and function. The squid and cuttlefish have 8 arms and 2 tentacles, the tentacles having both suckers and toothed or barbed structures. The octopus has 8 arms, though some biologists are pushing to have the 8 arms be called 4 arms and 4 legs, based on the way they sometimes use them when moving across the bottom. The arms of the octopus lack the peduncles that tentacles have.)
Octopuses are amazing creatures. A full-grown (~100 pound) Giant Pacific Octopus can fit through about a 3" opening (about the size of a condensed soup can.) They are extremely intelligent (especially for a mollusk!); can learn to run a maze, open a jar or childproof pill bottle, and even remember faces over a long term. I volunteer at the Seattle Aquarium and one of the really fun parts of the job is feeding the Giant Pacific Octopus. We had an octopus that took about an hour to figure out how to open a peanut butter jar with food in it the first time it was given to it. His personal record was 45 seconds, before he was released back to the wild.
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