While the earliest date can be disputable, big shift can be pinpointed as the Transmeta Crusoe CPU release in 2000.
Transmeta was a secretive company working since 1995 on a "mystery product", employing some celebrities from the IT world (like Linus Torvalds.) Its "mystery product" was a new CPU with focus of power consumption. It offered unprecedented battery life to laptops.
The fame of the company was short-lived. Crusoe, while revolutionary, didn't entirely perform to promised specs. It was fairly expensive for what it offered performance-wise and it had minor compatibility problems with x86 platform. Still, the idea caught on, and both Intel and AMD released their own "low-power" CPUs soon after (putting the last nail in Transmeta's coffin.)
For a time the development ran in parallel, high-performance, high-power CPUs for desktop, and "energy-saving" portable CPUs. The manufacturers ran against a wall when trying to maintain Moore's Law concerning CPU speed though - power consumption for anything exceeding 4GHZ was excessive, and heat dissipation was difficult.
That's where the race for higher clock speed ended, and the race for more cores in one chip began. Simultaneously, lower clock speeds allowed, and heat dissipation problems necessitated reduction of power consumption and tout that as a marketing point, "energy efficient".
Another high point in the race for energy efficiency was the One Laptop Per Child project.
OLPC, starting around 2005, was a non-profit developing special child-friendly laptops with many completely novel solutions - including a system-on-chip, Geode processor, with power demand low enough that the laptop could be charged by an attached crank.
One of points of the program was "Give one, get one" - the system would be unavailable in normal trade, except this program: buy two, one goes to a child in need in a 3rd world country, you keep the other.
Asus, tasked with development of the device, did something rather mean - using the experiences gained developing OLPC XO-1, created Asus EEE PC - the first netbook. The price, while higher than of a single XO-1, was still lower than that of two, the new competition murdering the OLPC G1G1 program, and the new fad for netbooks started - with EEE 901 ('2008) boasting over 9 hours of battery life using Intel Atom. Along with iPhone (2007), Google G1 (2008) and iPad (2010) the race for "super-low-power CPU" began for real, and ARM became a major player.