"Stars" and "Eyes" in gemstones are the result of the reflection of light on tiny needle or tube-like inclusions.
Gemstones that only have one set of needles will show an eye. For example, Chrysoberyl Cat's Eye.
In sapphire, there are 3 sets of needles (oriented in 3 directions) intersecting at 60/120 degrees. Think of an asterisk! When cut and polished correctly, this results in a lovely star that makes star sapphires so captivating.
How do these needles form in sapphire? During the formation of the sapphire crystal, high temperatures allow impurities to mix into the solid solution. As the solution cools and the crystal forms, these impurities may crystallise out in a specific pattern within the host sapphire. This "unmixing" process is called "exsolution". In sapphire, rutile is unmixed to form the needles that give rise to a star!
I've kept my answer short and simple. If I missed something or if you need a more detailed explanation, drop me a message and I'd be glad to help. I recommend these books if you are serious about sapphires and gemstones: Richard Hughes "Ruby & Sapphire"; Webster's "Gems".