(1) This verse is taken as a pious start to Raamaayan, for any epic has to have a good pious beginning, pious middle and pious ending. Thus this verse has the letter maa at its start and "maa" is Lakshmee vaach in Sanskrit. The first letter - loka maataa maa ramaa mangal devataa thus Amar Kosh says for Goddess Lakshmee.

maa= Goddess Lakshmi;
niÿaada= Oh! Vishnu [for Goddess Lakshmee resides in the heart of Vishnu - niÿadŸti asmin iti niÿ˜da ];
yat = by which act;
kraunch midhunaat = the couple of demons, namely Raavan and Mandodaree;
kaam mohitam = that impassioned one and stole Seetaa;
ekam= that one, Raavan;
avadhee = you killed; by that act of yours þaþvateesamaa = everlasting for ages;
pratiÿ÷aam = divine sanctity;
tvam agam = you, get.

"Goddess Lakshmee's abode... Oh! Vishnu, by which act of your killing one male demon named Raavan, who in his passion abducted Seetaa, and thus you eradicated the vice from the earth, for that you get an everlasting divine sanctity, as Raam, for ages to come."

(2) There is another declination attributing this to Raavan. Raavan is the one who tortures others for his benefit.
itaraam saadayati peeDayati iti nishaad - thus: Oh! Raavan;
kraunch+mithunaat = from the couple of Raam and Seetaa, who are flying from forest to forest like nest-less birds;
ekam= one is, Seetaa is;
avadhii = as good as killing [her with your torture of abducting;
pratishthaam= your glory in Lanka, at its zenith, as per the kindness of Brahma;
ma+agama= never get, hereafter.
But this declination is not held right, for it is like a curse, shaap, and no epic shall start with a bad omen.

(3) Next, this verse is said from the perspective of Raam alone. Sage Naarad gave the details of the legend to Sage Vaalmeeki and Brahmaa Jee orders that the legend of Raam is to be recorded. But Raamaayan is full of pathos (karunaa - shok rasa pradhaan). If it is to be penned, the writer too shall have heart that can outpour that mood. So when Vaalmeeki is at the river bank, Raam, say Vishnu, came in the guise of a tribal, as with other mythological episodes like Kiraataarjun etc, and killed one bird. Vaalmeeki reacted immediately and Vishnu's test is complete. But in excitment, the mood of such holy sage, Raam gets a curse in this verse - maa nishaada.

nishaad = oh tribal: to Vaalmeeki / Vishnu to mythology; for your killing one bird of the couple, to the misery of the female one;
shaashvatee = as long as you live on this earth;
samaaH+pratishthaam= togetherness, with your wife;
ma+agama = do not get.

Oh! Raam, as long as you are on Earth, you do not get the love of being together with your wife... for you have to live with your wife departed [to Lankaa] come again and departed [to forests.]

But this is differed statement, since Vishnu does not require any personal testing of the capabilities of the writer of Raamaayan. Brahmaa will look after such literary things.

(4) The generally accepted meaning of this verse is this. Any epic's gist is to be said at the start or, at its commencement, thus the above verse included the meaning of whole of the epic, Raamaayan.