Once you have defeated Whitney, you can do something about the tree blocking the path on Route 36. Go get the squirt bottle from the Goldenrod flower shop if you haven't already. Then go to Route 36 (you can get to it either by going east from the National Park, or by going West from Violet City), and use the squirt bottle on the tree.
It will wake up and reveal itself to be a pokémon! This Sudowoodo is the only one in the game, so be sure to catch it rather than KOing it.
Once you have caught or KOed the Sudowoodo, the path to Ecruteak City is opened. On the way there, you will have some trainer battles. You can also find a small alcove where three Apricorn Trees grow.