The Definitive Edition introduces some much-needed "Quality of Life" improvements:

Rebuilt lighting systems, improved shadows, and high-resolution textures.

For many gamers, the drop into Liberty City wasn’t with the HD graphics of GTA IV or the online chaos of GTA V . It started with a silent protagonist, a yellow taxi, and a cell phone call that changed gaming history: “My name is Catalina. Remember that, because you’re gonna be hearing a lot of it.”

to improve the performance and graphics of the Definitive Edition? Grand Theft Auto III - The Definitive Edition on Steam