Most regulators require the input voltage to be between 2V to 3V higher than the rated output voltage, this is called the drop-out voltage, for example for an LM7805 has a drop-out of 3V so to provide you with 5V at 1A you need an input voltage of at least 8V. Low dropout voltage regulators are as the name implies regulators with a very low drop-out voltage, typically less than 1V, but you can get fairly inexpensive regulators with drop-out voltages as low as 300mV.