The name Wadō-ryū has three parts: Wa, dō, and ryū. Wa means "harmony," dō means "way," and ryū means "school" or "style". Harmony is simply the acknowledgment that yielding is sometimes more effective than brute strength.
From one point of view, Wadō-ryū might be considered a style of jujitsu rather than karate. The founder, Hironori Ōtsuka, was a licensed Shindō Yōshin-ryū practitioner and a student of Yōshin-ryū when he first met the Okinawan karate master Gichin Funakoshi. After having learned from Funakoshi, and after their split, with Okinawan masters such as Kenwa Mabuni and Motobu Chōki, Ōtsuka merged Shindō Yōshin-ryū with Okinawan karate. The result of Ōtsuka's efforts is Wadō-ryū Karate.
To the untrained observer, Wadō-ryū might look similar to other styles of karate, such as Shito ryu or Shorin ryu. Most of the underlying principles, however, were derived from Shindō Yōshin-ryū, an atemi waza focused style of Jujutsu. A block in Wadō may look much like a block in Goju/Uechi ryu, but they are executed from different perspectives.
A key principle in Wadō-ryū is that of tai sabaki (often incorrectly referred to as 'evasion'). The Japanese term can be translated as "body-management," and refers to body manipulation so as to move the defender as well as the attacker out of harm's way. The way to achieve this is to 'move along' rather than to 'move against'—or harmony rather than physical strength.
As with other styles of karate Wadō-ryū techniques move from the heels of the feet, but differ in that many (particularly the gyaku zuki reverse punch, like a boxer's cross) progress to incorporate pushing off the ball of the foot as well. This affects the delivery of a number of techniques, particularly adding reach to punches with the back hand, given the extra hip movement afforded utilising the balls of the feet in this fashion.
While the core principles (at least with regard to transmission of body weight into punches) of turning on the heel remain in Wado, as it is the fastest way to push the hips in the direction of attack, the progression to the ball of the foot is a hallmark of the style. It is important to remember that this in no way makes it superior or inferior as a system in comparison to other styles, it is simply another way of thinking that has both merit and drawbacks.