There are several reasons why Clapton coils are so popular: they can increase flavor, increase cloud production, they have better longevity, they can look cool and are fun to make.
The increased cloud production is caused by the large increase in surface area. All of the nooks and crannies of the outer wire creates increases the surface area of the otherwise bare wire by quite a bit. This increased surface area is essentially exposing more wire to juice which allows it to heat a larger amount of juice at the same time, increasing vapor production.
This is partially why a Clapton coil can have more flavor as well. The flavor from a Clapton coil can have more depth to it since they allow you to taste more notes in your juice. Think of it this way: at certain temperatures, different notes of your juice come out which is why it is good to adjust your power a little bit every time you change flavors. In a Clapton coil, the core will heat up much faster than the outer wire, allowing you to taste flavors that come out at higher power levels at the same time you taste flavors that come out at lower power levels at the same time.
Clapton coils also act as a wick and stores juice inside its cavities. Some variations have interesting wicking properties such as the Alien Clapton, invented by blueeyedgoon89 on Instagram; this wire will disperse the juice throughout the wire when wet.