Modern-day presidents are powerful men. This was not always the case, though. The Founding Fathers were leery of executive power, so they designed a government with three discrete and equal branches. In general, presidential power has been steadily enhanced throughout American history by a number of factors.
One reason for increased executive power is precedent. George Washington, the nation's first president, was cautious in his approach to the office. He and his countrymen had fought a war against monarchy, so he was reluctant to claim too much power. Theodore Roosevelt, on the other hand, was a larger-than-life figure. His forceful personality invigorated the presidency. I believe most modern presidents have been more like Roosevelt than Washington.
A second reason for the vigor of the modern presidency is television. John F. Kennedy is generally regarded as the first TV president. His charisma and attractiveness on the small screen ushered in the "Age of Camelot." Modern-day presidents can go on TV in order to rally the public behind them.
National emergencies have also contributed the enhancement of presidential power. For example, the Civil War and the Great Depression threatened the nation's survival, so presidents took unprecedented actions to stave off disaster. National crises buttress a vigorous presidency.