You will need:
Rock candy crystals
You made a supersaturated solution of sugar and water! The sugar crystals could only stay dissolved whilst the water was hot. Cooling the solution down made it super-saturated, which is unstable. As water cooled down less of the sugar crystals could remain in the water and so they began to settle out onto the kebab stick, which effectively acted as a seeding crystal. More and more of the sugar continued to settle out of the solution onto the kebab stick and so your crystals continued to grow!
The longer it takes to form a crystal, the larger the crystal will be.
This works whether you are talking about crystal growing kits, making liquid nitrogen ice-cream or gemstones!
Check out the link on crystals formed by volcanoes; Indianapolis Childrens Museum
Similar experiment: Borax crystal snowflakes