If a banker wants to move money between two accounts, there are actually two operations: take the amount from one of the accounts and add it to the other one.
For these operations to be considered atomic, they need to happen both or none of them. If money is added to one of the accounts, but the reduction in the other one does not go through (not enough funds, for example) the first operation needs to be taken back.
For them to be considered isolated, nobody else should be able to check out the balances of the accounts after one operation but before the another one. Results must be available as one.