Each task in your schedule is either Automatic or Locked, shown in the Auto? column.
Automatic is the default. The task starts as soon as the tasks it depends on are finished, and it moves whenever those predecessors move. This is what keeps your whole schedule in sync.
Locked means the task holds the specific date you set. Auto Scheduling will not move it, even if an earlier task runs late. Useful for dates that are set in stone, like a contractor's confirmed start date.
If a task will not move when you expect it to, check whether it is set to Locked. Toggling it back to Auto lets it move with its dependencies again.
Read the full article: What's the difference between an Automatic and a Locked task?