The term “milk” continues the analogy begun with the concepts of birth and reborn infants. The adjective “pure” wants the milk to be uncontaminated. The term “spiritual” translates a Greek word from which we get the English word “logical.” That is also the point Peter is making here; he instructs his readers to crave the logical, obvious kind of “milk” their rebirth (and hence status as newborns) requires. As the one causing their rebirth was God (1 Peter 1:3), so the source of the sustenance they need to support their new life must obviously be God. Their craving must be him, and he feeds and nourishes his (newborn) children through the heavenly breast of the Word and its preaching.
2 Like newborn infants, long for the pure spiritual milk, that by it you may grow up into salvation