What is the "successive-configuration relation"? This term is used in the book Foundations of Cryptography on pg 20 with regard to defining deterministic oracles, but is not previously defined and I can't seem to find a definition online easily.
OK, let's first observe the usage of the word in-context:


  Definition 1.3.8 (Oracle Machines): A (deterministic/probabilistic)
  oracle machine is a (deterministic/probabilistic) Turing machine with
  an additional tape, called the oracle tape, and two special states,
  called oracle invocation and oracle appeared. The computation of the
  deterministic oracle machine $M$ on input $x$ and with access to the
  oracle $f:\{0,1\}^*\to\{0,1\}^*$ is defined by the
  successive-configuration relation. For configurations with states
  different from oracle invocation, the next configuration is defined as
  usual. Let $\gamma$ be a configuration in which the state is oracle
  invocation and the content of the oracle tape is $q$. Then the
  configuration following $\gamma$ is identical to $\gamma$ , except that the state is
  oracle appeared, and the content of the oracle tape is $f(q)$. The
  string $q$ is called $M$’s query, and $f(q)$ is called the oracle reply.
  The computation of a probabilistic oracle machine is defined
  analogously. The output distribution of the oracle machine $M$, on input
  $x$ and with access to the oracle $f$ , is denoted $M^f(x)$.


So the context we have is: Turing Machines!

Now if we look at the formal definition of a turing machine, we will spot a relation $\delta:(Q\setminus F)\times\Gamma\to Q\times \Gamma\times\{L,R\}$. Note how a function is actually just a relation.

This above function defines, when in a given state and looking at a given cell content, which cell content shall be written, where state shall be entered and which direction the head shall be moved. Thus, this relation defines the successive configuration for every configuration. However I'd guess that the relation used for the turing machine in question is a little bit more complicated than the one of the "basic" turing macine (also accounting for the special states and the extra tape).