Taking the literal approach (note that "jetzt heißt es" is an inversion of "es heißt jetzt", sounding a bit more poetically):
- "Jetzt" = "Now"
- "es heißt" = "It's called" / "Its name is"
So far, so good. But what does "es" refer to? It's the activity to be done by the addressee(s)!
To piece it together: "Now, the activity we/you should do is (called) X", or more colloquially: "Now, we/you should do X".
Note that whether "we" or "you" is used depends on whether the speaker includes himself in said activity (a teacher saying "Jetzt heißt es aufpassen!" will likely not include himself, whereas a colleague saying "Jetzt heißt es Mittag essen!" probably wants to eat lunch, too).
In general, this idiom is used to convey an action that has to be done without using imperative directly (which can be considered impolite in many circumstances) or to convey an action that is inevitable ("Jetzt heißt es Abschied nehmen." - "Now we have to say farewell."). It's also a passive call to action, omitting the original caller so the speaker is able to distance himself from the order - even if he is the one who calls it (maybe he doesn't like it, or he has to do it because of rules so it's not his decision).
To look at your example phrases:
Jetzt heißt es aufpassen!
Now you'll have to pay (close) attention (, because what I'll tell you next is important)!
Nun, jetzt heißt es "alle Mann an Deck", Miguel.
Well, now we have to go on deck, Miguel.
or, more colloquial/keeping in line with the original
Well, now the order is "all hands on deck", Miguel.
EDIT: Of course, there's always the literal use: "Jetzt heißt es 'Bundesagentur für Arbeit' (statt Arbeitsamt)" - "Now it's called 'Bundesagentur für Arbeit' (instead of 'Arbeitsamt')" (= the German Federal Employment Agency)