In an absolute monarchy, the ruler's powers are unbounded by law; he simultaneously has executive, legislative and judicial powers without any checks or balances.
In a constitutional monarchy the monarch's powers are delineated by a (written or unwritten) constitution. Most constitutional monarchies severely curtail the ruler's powers, up to many modern democracies, such as the United Kingdom or Sweden, where the monarch's role is mostly ceremonial. In contrast, Germany before World War I and Japan before World War II had written constitutions which guaranteed their emperors significant political power.
For example, in Great Britain, while the Queen is technically required to approve any legislation made by Parliament passes into law, no king or queen since Queen Anne has ever withheld such approval. The queen also has regular audiences with the Prime Minister and visiting foreign leaders.