Yes. Every PlayStation 3 model (Fat, Slim, Super Slim) includes a Blu-ray drive and native playback support for commercial Blu-ray movies. This was a major selling point at launch (2006), as standalone Blu-ray players cost $500–$1,000.
If playback fails: update system software, clean disc, try another Blu-ray. Drive laser failure is common on early "fat" models (KES-400A).