It literally means that it is possible to see a crescent bright moon with a paler image of the rest of the moons surface filling in within the arms of the crescent. The Earth is reflecting back moonlight from the crescent to illuminate the "dark" portion of the moon. I can't remember the poem (it been a few years/decades) so I won't comment on the symbology, but it is a real phenomenon. See http://apod.nasa.gov/apod/ap020419.htmln and others....
this line comes from the famous ballad, "Sir Patrick Spens". these are the surrounding stanzas:
"Make ready, make ready, my merry men all,
Our good ship sails the morn."
"Now, ever alack, my master dear
I fear a deadly storm.
"I saw the new moon late yestreen
With the old moon in her arm;
And if we go to sea, master,
I fear we'll come to harm."
They had not sailed a league, a league,
A league but barely three,
When the lift grew dark, and the wind blew loud,
And gurly grew the sea.
The ankers brake and the top-masts lap,
It was such a deadly storm;
And the waves came o'er the broken ship
Till all her sides were torn.
flyyakker did a good job of explaining the literal meaning of the lines in question. as far as the poem goes, the significance is in the dangerous signs that have been given by nature. remember that Sens has a long and risky voyage to cover over the (winter) sea.
sailors have always had to read the natural world around them to predict the weather they will be facing (or otherwise choose to avoid). the moon influences tides on earth, and it also influences the seas he will be sailing. as we find in the rest of the poem, the prediction was right; they meet with a deadly storm and lose their lives because of it.
here is a little explanation from wikipedia:
"Nearly all versions, whether they have the wreck on the outward voyage or the return, relate the bad omen of seeing 'the new moon late yestreen, with the auld moon in her arms', and modern science agrees the tides would be at maximum force at that time."
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