The include relationship allows one use case to include the steps of another use case.
For example, suppose you have an Amazon Account and you want to check on an order, well it is impossible to check on the order without first logging into your account. So the flow of events would like so...
The extend relationship is used to add an extra step to the flow of a use case, that is usually an optional step...
Imagine that we are still talking about your amazon account. Lets assume the base case is Order and the extension use case is Amazon Prime. The user can choose to just order the item regularly, or, the user has the option to select Amazon Prime which ensure his order will arrive faster at higher cost.
However, note that the user does not have to select Amazon Prime, this is just an option, they can choose to ignore this use case.