In the example hand you have a flush draw and pot is $1500 and it will cost $500 to call. Your expressed odds are 3 to 1 and you are about 4 to 1 to hit the flush so on the face of it a call has negative expectation based on expressed odds. However if you hit your flush draw you could win another bet on the river. If you bet $500 when you hit your flush the implied odds are 4 to 1 if he calls your river bet 100% of the time.
What the book is explaining is that your implied odds in this case are not 4 to 1 as an opponent will not always call your $500 on the river. This is why you must multiply by the probability of the call for example;

If flush card hits and I bet $500 I think my opponent will call 75% of the time. $500 x 75% (probability of call) = $375. Implied odds are $1500 + $375/$500 (value of turn call) = 3.75 to 1.

If flush card hits and I bet $1000 I think my opponent will call 60% of the time. $1000 x 60% = $600. Implied odds are $1500 + $600/$500 = 4.2 to 1.

If flush card hits and I bet $2000 I think opponent will call 40% of the time. Implied odds are $2000 x 40% = $800. Implied odds are $1500 + $800/$500 =4.6 to 1

Therefore in these examples if your flush card hits a $2000 river bet is better than a $500 bet as it has higher implied odds even though your opponent is more likely to fold.