what _could_ he mean?

"You can call yourself my 'Father Confessor,' you know, if you entertain
any scruples as to the propriety of a staid old bachelor's fathering a
stray young cub like me--that will make it all right, surely! You will
let me, won't you? In all the world there is no one so close to me as
you, and such dreams as I may happily bring to fulfillment will be, more
than you know, because of your guidance, your inspiration. You are the
father of my spirit, whoever may have been the father of my flesh! Let
it be hereafter, then, not 'Uncle,' but 'Father Paul'!"

And the older man, rising and standing by the Boy, threw his arm around
the young shoulders, and gazing far off to the distant west, felt
himself shaken by a strange emotion as he answered, "Yes, Boy, hereafter
let it be 'Father Paul!'"

And as the sun travelled faster and faster toward the line of its
crossing between the worlds of night and day, its rays reflected a new
radiance upon the faces of the two men who sat in the silent shadows of
the park, feeling themselves drawn more closely together than ever
before, thinking, thinking, thinking-in the eyes of the man a great
memory, in the eyes of the Boy a great longing for life!

* * * * *

The two friends ran up to London for the theatre that night, to see a
famous actor in a popular play, but neither was much interested in the
performance. Something had kindled in the heart of the man a reminiscent
fire and the Boy was thinking his own thoughts and listening, ever
listening.