Albert Barnes on Luke 1:80

Waxed strong in spirit. That is, in courage, understanding, and purposes of good, fitting him for his future work. The word wax means to increase, to grow, from an old Saxon word.

In the deserts. In Hebron, and in the hill country where his father resided. He dwelt in obscurity, and was not known publicly by the people.

Until the day of his showing. Until he entered on his public ministry, as recorded in Mt 3; --that is, probably, until he was about thirty years of age. See Lk 3.