Hi Simon,
To put it simply cases are a collection of activities and activities have 4 types in F&O: Action, task, appointment and event.
create an action, which is a unit of work that is completed in the past
A task, which is a unit of work that is to be done in the future
To create an appointment, which is a scheduled meeting
To create an event, which is something that has already occurred
As standard activities, when created, are typically linked to a specific document e.g. overdue invoice. However, if you wanted to track activities performed for chasing a number of invoices e.g. the customer is having financial difficulties rather than an issue with a single invoice, then you would create a 'case' and track the activities at the case level rather than recording them on the individual invoices.
Hope this helps.