Cash basis means you don't book anything until cash is exchanged. So, if a customer pays with a credit card the transaction wouldn't immediately be recorded (because you haven't been paid by VISA or whoever).
Accrual basis means you book transaction with the assumption x will occur. So your same customer pays with credit, but instead of waiting until you receive cash you book a receivable (Accounts Receivable).
Modified, I assume is just a combination of the 2. Not sure what to tell you.
The difference between the two is really just timing.