The over-simplified explanation is that a switching regulator works kinda like the PWM you're using to drive the LEDs: instead of turning the extra input voltage into heat, it turns it off and on very fast so the average output is the voltage you want.
The three key things you need to know are that they're more efficient, more expensive, and that some of them don't work correctly unless you have a minimum load. E.g., a 5V 5A power supply might not give you a clean 5V if your system only draws 100mA. Since your LEDs will probably have some "all off" time, you need to check the specs on any regulator you're considering to make sure it doesn't require a minimum load.