Conductivity is all about how well energy travels thru a material. In the case of crochet hooks it’s about how well that material conducts heat.
One thing that can affect how comfortable a hook is in your hand is the material it is made from. If your hook is sucking all the heat from your hands, it could increase your risk for repetitive stress injuries.
For some crocheters, there is no real worry about conductivity. They don’t spend hours on end stitching. Their time with the hook is interrupted and intermittent. That is actually a good thing. Because it means breaks are sort of “built in” to their stitching time.
But what about folks that spend a couple of hours at a time stitching or those who are plagued by arthritic pain in the hands? Then the material their hook is made of can make a world of difference.

Metal hooks are the big culprit when it comes to discomfort crocheting. They are also the most commonly available and affordable hooks out there. In the US particularly, the aluminum hooks manufactured by Susan Bates and Boye are the most frequently sold hooks.
Any kind of metal though is a great conductor of heat. And heat is something you need to keep in your hands to avoid repetitive stress injuries or arthritic pain.
Personally I love metal hooks. They tend to be smooth and fast with most yarn fibers. They are also durable, especially when it comes to working with non-traditional materials. It works much better to crochet wire with a metal hook as opposed to using a wood or plastic one.

This is one of the reasons that I like my Clover Soft Touch and Tulip Etimo hooks so much. I get the best of both worlds. Metal hook with a warmer less conductive handle. But they can be daunting to some crafters as the individual cost per hook is about 3 times that of regular metal hooks.

Susan Bates also has a hook series with Bamboo handles that I’ve heard good reports about. My hook hold is such that they aren’t that ideal for me, though I need to use them a bit more to decide if I would recommend them.
If you are only working with yarn, then wood or plastic hooks could be fine for you.

A very affordable option for a wood hook are the bamboo hooks from ChiaoGoo, they come in a wide range of sizes and are often my choice for design projects that need a larger gauge hook.

The Laurel Hill hooks are lovely if you are willing to pay a bit more. They sit beautifully in the hand and are finished super smooth to glide thru any yarn fiber you want to work with. They do have a very tapered throat, so that can make gauge a little trickier.

My favorite plastic hooks are from Clover. They currently are only available in sets of 3 hooks. Size N, L, & K and Sizes J, H, & G are packaged together in a handy and decorative tube. They are not as smooth as the other hooks I’ve mentioned, but they are quite serviceable and the shape is very hand friendly as well as the plastic will warm up to your touch without cooling off your hand.

If you are more of a DIY kind of crafter you can always modify your hook. I have an article at the Crochet Uncut website on using shelf liner to add width to your hook. Making a Hook Friendly.