I don't have the full text of the 3rd edition here, but from the context you've posted, it's clear what he's saying.
Imagine a kind of 'vector' class.
class Vector {
private:
int * data; // pointer to data
There are several ways it could provide access to the vector size:
Choice 1: a public member variable:
public:
int datasize;
Choice 2: a private variable with a public accessor
private:
int datasize;
public:
int getSize(); // body can be hidden in CPP, but would be { return datasize;};
Choice 3: as 2, but with an inline accessor
private:
int datasize;
public:
inline int getSize() { return datasize; };
Now, #1 has poor data hiding, but great performance. #2 has great data hiding, but poor performance. #3 has good data hiding, and possibly great performance. (remember inline is just a hint)
In my view the data hiding of #3 is slightly inferior to #2 because the function code is revealed in the header - even if you can't access the member. So, I'd rewrite his statement along the lines of...
Inline Functions provide a good compromise between the requirements of Data Hiding versus Performance.
I wouldn't agree that it's of "primary importance", as it's just a hint to the compiler.