Sorry if that passage of the book was a bit cryptic. Here's the idea.

Suppose we start with a generic beta( theta | a=1 , b=1 ) "proto-prior".

Then, suppose we have some fictional data that express our prior beliefs, in this case getting 95% tails in 20 tosses. That is, we fictionally observe z=1 head in N=20 flips. If we update the proto-prior with these fictional data, we get

beta( theta | a+z , b+N-z ) = beta( theta | 1+1 , 1+19 ) = beta( theta | 2 , 20 )

as our new prior based on the fictional data.

It's the same process as if we had real previous data with z=1 and N=20, but here we have fictional data to express our prior beliefs. In general, it's often easier to express prior beliefs in terms of idealized data than in terms of parameter values...

Hope that helps.

And thanks for reading the book!