This chapter gives us an in-depth examination of the character of Ahab and what is known about him, and the considerable sense of mystery that surrounds him, especially relating to his scar and his fake leg. However, what is interesting is that the passage you have specified seems to detract from the rather grim description we are given of his character, showing that even the hardest individual (such as Ahab) can soften under the right circumstances:
Nevertheless, ere long, the warm, warbling persuasiveness of the pleasant, holiday weather we came to, seemed gradually to charm him from his mood. For, as when the red-cheeked, dancing girls, April and May, trip home to the wintry, misanthropic woods; even the barest, ruggedest, most thunder-cloven old oak will at least send forth some few green sprouts, to welcome such gladhearted visitants; so Ahab did, in the end, a little respond to the playful allurings of that girlish air. More than once did he put forth the faint blossom of a look, which, in any other man, would have soon flowered out in a smile.
Note the explicit comparison that is made between Ahab and the "barest, ruggedest, most thunder-cloven old oak" who will blossom in the right conditions. Ahab, despite his grim nature, is not immune to the effects of the "pleasant, holiday weather," and whilst he does not actually go as far as smiling, his rough exterior is certainly softened by the good weather that the sailors enjoy. I suppose the obvious link that we can make between this passage and our world today is the way in which every character has the capacity to enjoy and participate in simple pleasures, no matter how hard a personality they seem to have.