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Let's use the definition of “shaping” to explain successive approximations. Our definition of "shaping" is: "a behavioral term that refers to gradually molding or training an organism to perform a specific response by reinforcing any responses that come close to the desired response.
For example, a researcher can use shaping to train a rat to press a lever during an experiment (since rats are not born with the instinct to press a lever in a cage during an experiment). To start, the researcher may reward the rat when it makes any movement at all in the direction of the lever. Then, the rat has to actually take a step toward the lever to get rewarded. Then, it has to go over to the lever to get rewarded (remember, it will not receive any reward for doing the earlier behaviors now...it must make a more advanced move by going over to the lever), and so on until only pressing the lever will produce reward. The rat's behavior was 'shaped' to get it to press the lever."
In this example, each time the rat is rewarded, it is being rewarded for a "successive approximation", or for acting in a way that gets closer and closer to the desired behavior.