A computer application contains a number of different 'tasks', 'transactions', 'programs' or 'modules', each of which performs a particular function. Sometimes the processing of one particular task is supposed to be followed by one or more other tasks in order to complete some higher process. For example, the task 'Take Customer Order' may have to be followed by 'Charge Customer', 'Pack Order' and 'Ship Order'. This higher process may have a name such as 'Order Fulfillment', but as you can see it cannot be handled by a single task and has to be broken down into its component parts.
Without a workflow system the processing of the component parts has to be handled manually, which is where mistakes can occur. Forgetting to charge the customer or ship the order is not a good way to run a business.
With a Workflow system it is possible to define 'Order Fulfillment' as a workflow process, with 'Charge Customer', 'Pack Order' and 'Ship Order' as components of that process. When an instance (or 'case') of the workflow process is created the workflow engine will then take responsibility for dealing with each component in turn. These components may be executed automatically, or they may be directed to appear in someone's inbox.