Why is turning down the heat during day and night considered more efficient?
Your assumption is incorrect. More heat is lost when the difference between inside and outside temperatures is greater. So, if you keep the house at 72F (22C) it will lose heat faster than if you kept it at 62F (17C). Thus, your heater will need to run more often and/or for longer to maintain your desired temperature. It therefore uses more energy to maintain the higher set point than the lower set point. 

This effect becomes more pronounced the longer the lower set point is maintained, but may not be noticeable at all for short periods. However, it's important to note that it doesn't become less efficient if you turn down the heat for short periods, since the heater is not running at all while the house is cooling to the lower set point.

Heaters (and AC) in general do not have an intensity setting - they're either on or off. The energy from the sun does play into things a little bit, but not a whole lot and not really in the morning. Opening curtains during the day can certainly help to make the house feel warmer.

All of these effects apply in the summer, too, although then you want a higher set point when you're not home, not a lower one, close curtains during the day, etc.