Here is the full excerpt in a description of the Metropolis-Hastings algorithm (p.144), when contemplating a move from [current] $\mu=110$ to [proposed] $\mu=108$:
Compare the height of the posterior at the value of the new proposal
against the height of the posterior at the most recent sample. Since
the target distribution is normal with mean 100 (the value of the
single observation) and standard deviation 15, this means comparing $N(100|108, 15)$ against $N(100|110, 15)$. Here, $N(μ|x, σ )$
indicates the normal distribution for the posterior: the probability
of value $μ$ given the data $x$ and standard deviation $σ$.
Hence, we are in a situation where the targeted posterior is
as the prior density on $\mu$ is constant. Therefore, $N(μ|x, σ )$
denotes the normal density with mean $x$ and standard deviation $\sigma$. And the Metropolis-Hastings acceptance probability is
Let me add that the description is very poor, in particular because the author has inverted the roles of $\mu$ and $x$ in the sentence
this means comparing $N(100|108, 15)$ against $N(100|110, 15)$.
which should be
this means comparing $N(108|100, 15)$ against $N(110|100, 15)$.
Of course, mathematically, $N(100|108, 15)=N(108|100, 15)$, so the comparison is correct. But it unnecessarily confuses the reader.