When you need to receive all the notifications of a task or all the tasks inside a list, you must enable the watch option.
Of course, you can also receive all the notificattions when the task is assigned to you, but many times you are not the person who is supposed to do the task and therefore there is no reason for the task to be assigned to you, but you need to receive the notifications. For this reason, the watch option will be a very useful feature for you.
To enable watch for a task, open more settings in the task and select the watch option.
To enable watch for a list, open list settings and select the watch option.