The Nest probably pioneered the smart thermostat market in 2011.

The main benefits of a smart thermostat: It cust down on your energy bill. More importantly, you can control a smart thermostat remotely, from your phone, on your tablet, or with your voice. 

A smart thermostat is expensive than a normal thermstat, and people are buying the smart version because they can't learn / try to program a normal thermostat and remember to shut it off

Newer smart thermostats can even integrate into new smart home devices such as Amazon Echo etc.

The best smart thermostat for normal use: Nest Learning Thermostat (easy to use, good looking, smart learning capabilities)

The second best smart thermostat for normal use: Ecobee3 (more sensors for large houses, especially thjose with weak HVAC systems, support for Apple's Homekit)

The best affordable smart thermostat for normal use: Ecobee3 Lite (without sensors)