Chemically, there is virtually no difference between table salt, kosher salt, and fancy sea salt. All of them are close to 100% pure NaCl (sodium chloride), with a few trace elements thrown in. In the case of table salt, those ingredients are there to prevent it from caking.
Kosher salt is that it is much easier to pick up between your fingers, improving your control over your seasoning. It's large grains make it more effective at drawing out liquid from meat.
The biggest reason why chefs love to use kosher salt however is that it is much easier to pick up between your fingers, giving you tighter control over your seasoning. There's actually little difference between the two beyond the size of the salt grains (unless you are sensitive to iodine in table salt).
Regular table salt is comprised of many minute, regularly shaped cubes. This allows the granules to pack together tightly in a given space. Kosher salt, on the other hand, forms large, craggy flakes that don't fit together very well. Put them into a container, and you also end up with plenty of air space. What does this mean for cooking? It means that if you are measuring by volume, different types of salt are not interchangeable. A cup of table salt will have twice the salting power of a cup of kosher salt.