The name of the anthem is "Hatikvah", which is Hebrew for "The Hope". The lyrics are based upon the poem, "Tikvateinu" (Our Hope), written by Naphtali Herz Imber in 1878. Naphtali wrote the poem upon moving from the Austrian Empire to the land of Israel in 1870's. Even though he was a secular Jew, I think he did a wonderful job of capturing the 2000 year hope of the Jewish people - to someday return to Israel - their ancient homeland. The melody of Hatikvah was composed by Samuel Cohen in 1888. The tune is an adaptation of a popular Romanian folk song.
Before the modern state of Israel even existed, Hatikvah was first adopted as the theme song of the Zionist movement in 1897. It was later declared as Israel's national anthem in 1948, when Israel became a country. It wasn't until November 2004 that Hatikvah was officially sanctioned by the Israeli government as the country's national anthem.
Here is the English translation of the Hebrew lyrics:
Hatikvah - The Hope
As long as the Jewish spirit is yearning deep in the heart,
With eyes turned toward the East, looking toward Zion,
Then our hope - the two-thousand-year-old hope - will not
be lost:
To be a free people in our land,
The land of Zion and Jerusalem.
Here is a nice video version of Hatikvah. It includes both Hebrew and English subtitles, as well as some awesome scenery of the country: