Like difficult terrain, obstacles can hamper movement.
Obstacles Filling Squares: An obstacle such as a large tree, a pillar, or a floor-to-ceiling wall blocks a square entirely by completely filling it. You can’t enter a square that is filled by an obstacle.
Corners:When an obstacle fills a square, you can’t move diagonally across the corner of that square.
Obstacles Between Squares: Some obstacles run along the edges of squares instead of through squares. An obstacle such as a low wall between two squares makes moving from one square to the other just like entering a square of difficult terrain, even if the squares on each side of the wall are not difficult.
Published in Player's Handbook, page(s) 284, Player's Handbook 3, page(s) 220.