While he is often credited with creating the first synthetic plastic, he actually developed a material called Parkesine in 1855. Parkesine was a celluloid-like material made from nitrocellulose dissolved in camphor.
While it was the first synthetic plastic, it wasn't particularly practical and didn't achieve widespread use.
The invention of Bakelite, a synthetic thermosetting plastic, in 1907 by Leo Baekeland is generally considered the true breakthrough that led to the modern plastics industry.