This is a great question and one still being researched! Tentacles come in many kinds, and not all are sticky, but many are. Some jellyfish (such as the Lion's Mane jellyfish) even have tentacles up to 120 feet long! Each type of animal may use different methods of making their tentacles sticky, depending on what the tentacles are used for. Squid use their tentacles for grasping things such as food. Their tentacles are "sticky" in two or more ways. They are covered by a mucus that the squid makes, which is why squid in general are slimy. The real "stickiness" of squid tentacles, and their ability to hold objects comes from the suckers on the tentacle.

The suckers allow the tentacle to "stick" to prey or other objects. An example of suction would be like using a vacuum cleaner hose. In the same way that it can suck up dirt, the squid tentacles have hundred of small suckers that can hold onto prey. Here's a picture of one of the suckers with a Scanning Electron Microscope
picture here.

If you wanted, you could demonstrate this suction (with an adult helping you) by a simple experiment. Here's a video:
video here

If you put that open end of the bottle (as shown in this experiment) up to your arm and pressed the balloon in and out, the bottle would stick to your arm! Squids have hundreds of suckers that function like this, making their tentacles "sticky." Some big squid even have hooks inside their suckers, which is frightening.

Squid tentacles have suction cups on them that allow them to attach to things, and chitinous (tough, protective, semitransparent substance) "teeth" in those suction cups to actually hook into whatever they're holding onto. They're not really sticky - they're more complicated than just tentacles.

Actually, most squid and octopus tentacles actually have very strong "suckers" that act like suction cups for catching prey and grabbing at objects to help them move. The suckers themselves are not necessarily sticky, but because of their shape and the mechanism of the muscles involved in creating a suction, or partial vacuum, these organisms are able to "stick" to whatever they are trying to grab onto.

So how do their suckers work? First of all, the suckers are shaped like little bowls, and have several muscles in the "walls" of the "bowls." When the sucker is placed against a surface, the outer skin surrounding the sucker forms a seal around the sucker, so no water can get in or out of the "bowl." Then, the muscles in the sucker contract and make the volume inside the chamber slightly larger, which means there is still the same amount of water in a larger volume. This results in lower pressure inside the chamber, or a slight vacuum. Using this mechanism, squids and octopi are able to generate a pretty large "pressure differential" -- which means a pretty large difference in the amount of pressure inside the chamber formed by the sucker and outside of the sucker. The stronger the pressure differential, the stronger the suction, and the harder it is for prey to get away!