Modre is an older, more poetic word for a deep, clear blue, often used to describe eyes or the sky. While niebieski is the common word for blue, modre evokes a more vivid and almost literary image.
In the song, it's used to describe "modre oczy czyste od łez" (azure eyes clear of tears), painting a beautiful and somewhat melancholic picture of the captain's gaze. Its slightly archaic feel makes it stand out and adds a touch of classic Polish poetry to the lyrics.
The captain in the title turns up exactly once, and he is missing: "Kto wie, do jasnej, gdzie kapitan był" (who on earth knows where the captain was). Before that, sanah gives us a man who has run out of ways to quiet things down. His eyes are dry, his heart is loud, and "A tego już nie zagłuszy whisky i gin" (and whisky and gin can't drown this out anymore). "Życie od zawsze mu wieje pod włos" (life has always rubbed him the wrong way), so he tosses a coin and lets fate answer what he can't.
The chorus is the other voice in that room, and it is stubborn rather than soothing. "Będę przy tobie na amen" (I'll be by your side forever). "Sztormy nie dogonią nas" (the storms won't catch us). Then the line that does the real work: "Na płacz jeszcze mamy czas" (there's still time for crying). Not "don't cry", just not yet. By the bridge the whole promise has shrunk to "W triumfach, w klęskach / Na amen ty i ja" (in triumphs, in defeats / forever, you and I). It is a sea song in which nobody is actually steering, and that seems to be the idea: the ship is the two of them.