Who was the girl Jacob met in the park?

I think you're refering to Lizzie. She was pretty, knew about cars, and she was nice enough to care if Jacob (a stranger) was ok. He was hoping to imprint on Lizze who seemed to be interested and his type. He also wanted to forget about the impossible love he had for Bella. Unfortunatlly he did not inprint and he imprints on Renesme.