Kimi -the emperor, or one's lord. (Also an informal word for 'you', see Tale of Genji).
In the new Constitution of 1947, the emperor no longer was a sovereign who ruled by divine right.
Definition acc. new Constitution, affirmed by 1999 premier Obuchi: kimi means "the emperor as the symbol of Japan," and the entire lyric "wishes for the peace and prosperity of Japan."
Furhtermore, "kimi ga yo" "indicates our State, Japan, which has the emperor enthroned as the symbol of the State and of the unity of the people by the consensus-based will of Japanese citizens. And it is reasonable to take the lyric of "Kimi ga yo" to mean the wish for the lasting prosperity and peace of such a country as ours."

The explanation by Premier Obuchi obscures the simple beauty of the original poem.

A more literal translation of the poem, approximate meaning at the time of composition of the original 31 syllable poem:

May the reign of the Emperor
Continue for a thousand, nay, eight thousand generations,
And for the eternity that it takes
for small pebbles to grow into a great rock*
ans become covered with moss.

http://japanese.about.com/library/weekly/aa030400.htm

*an old legend about a certain kind of rock that can grow.