Westernesse blood

[lothiriel]

I can't find any topic about this, so here I go:

In RotK in the chapter Minas Tirith, Gandalf says to Pippin about Denethor:

He is not as other men of this time, Pippin, and whatever be his descent from father to son, by some chance the blood of Westernesse runs nearly true in him; as it does in his other son, Faramir, and yet did not in Boromir whom he loved best.

What does that mean?