I'll take a best exmaple to explain.
Statefull sessionbean : ATM operation
Stateless Session Bean : Credit card
Once we log into the ATM by entering PIN number. We can do multiple transacations like Balance enquiry, Withdrawl, ministatement..etc... For every transaction to client state is maintained and not required to enter for each transaction.
Coming to credit card operation.. There is only one transaction possible and for next transaction u required to authenticate again means no client state for second transaction...hence it is stateless