The global plan can't see everything
A global path planner, the kind covered in Motion Planning & Trajectory Optimization, computes a route across the entire known map from start to goal. It does this assuming the environment is mostly static and mostly known, which is a reasonable assumption for walls, shelving, and other fixed structure. But it is a terrible assumption for a person who steps around a corner three seconds before the robot gets there, a cart someone left in an aisle an hour ago, or another robot cutting across the same intersection. The global plan was computed once, over a map that is already slightly out of date by the time the robot is halfway along it.
This is exactly the gap that local obstacle avoidance fills. It operates on a much shorter time horizon, typically a second or two ahead, and a much smaller area, usually just the space immediately around the robot that its sensors can currently see. It doesn't try to find the best route to the goal. It tries to keep the robot safe and roughly on track for the next few moments, reacting to whatever the global plan couldn't have known about when it was computed.