Given a normal prior with mean $\mu_0$ and variance $\sigma_0^2$, and a normal likelihood with known variance $\sigma^2$, the Bayesian posterior, after observing $n$ iid signals $x_1,\dots,x_n$, is also a normal distribution with mean $$ \left(\frac{\mu_0}{\sigma_0^2}+\frac{\sum_{i=1}^nx_i}{\sigma^2}\right) \left(\frac{1}{\sigma_0^2}+\frac{n}{\sigma^2}\right)^{-1} $$ and variance $$\left(\frac{1}{\sigma_0^2}+\frac{n}{\sigma^2}\right)^{-1}.$$ See https://en.wikipedia.org/wiki/Conjugate_prior#Continuous_distributions.
Pratt, Raiffa, and Schlaifer (2008) suggest that we could define $$n'=\frac{\sigma^2}{\sigma_0^2}$$ so that the posterior mean and variance can be written as $$ \frac{n'\mu_0+\sum_{i=1}^nx_i}{n'+n}\quad\text{and}\quad\frac{\sigma^2}{n'+n}. $$
They say that
The parameter $n'$ can be interpreted therefore as the "fictitious sample size" or equivalent number of sample observations that describes the amount of information implicit in the prior distribution.
I'm having difficulty understanding the interpretation of $n'$, especially the part after "or". Could anyone help me understand it, by perhaps putting it in a different way, or elaborate it a little?