The process of upgrading a skill is much like enhancing a creature normally. You use special essences, or skill upgrade cards, which are drawn from a new Altar, which give EXP to a particular skill.
In order to upgrade a skill, you'll need an essence that corresponds to that particular skill. For example, in order to upgrade Pyre, you will need a Pyre Essence. Also, the star rating of the essence must be equal to the star rating of your card, and the level of the essence must be equal to or above the level of your card's ability. So, in order to upgrade Gemini'sPyre 10, you must have a 5-star Pyre Essence that is at least level 7 or higher. Using a Skill Essence any lower than 3 levels below the skill that you are trying to upgrade will result in no experience gain.
IGG likely implemented this feature in order to increase deck variety, and to give players a challenge whenever future maps are introduced. Maps 13 and 14 came out not long after Runes did, and the only reason why they're harder than previous maps is because of the Runes. So, my hypothesis is that IGG introduced higher skill caps to increase the difficulty of maps 15 and 16, where we begin to see skills like Dodge 15, Pyre 15 and Battleblow 15.