Each of your heroes has an individual Skill Rank, shown with the star symbol next to each hero. The Skill Rank is used to find opponents during matchmaking (How does matchmaking work?) and charges your Victory Bonus.
Every hero starts with a Skill Rank of 1. If you win matches the Skill Rank of this hero might increase. If you lose matches, the Skill Rank can go back down.
Since you are fighting against opponents of a similar Skill Rank, the Skill Rank is likely to increase if you play better, find stronger combination of spells or if you get more powerful by leveling up your hero and spells.
You can see your current and the best Skill Rank of a hero in the Spell Collection.
Till around Rank 35 (there are some exceptions) you normally need around 2 wins in a row to advance to a higher Rank. Once you reach a very high Rank there are fewer players and heroes with that Rank and therefore the wins in a row increase for the next Rank up.
The highest Skill Rank in the game is 50.