That's a really good question!

What makes it especially good is the strangely symbiotic relationship that the language of Hebrew and Zionist movement for a state of Israel had, that you touched on.

The revival of Hebrew as a spoken language is "in many ways unique in the history and evolution of language", according to Chaim Rabin. While it was used for liturgical studies and in some isolated cases, it did not have a hold anywhere in the world as a commonly spoken language (particularly in the homes of Jews), obviously due to the lack of a Jewish state and the widespread dispersal of Jews. In 1879, Rabin writes, Eliezer Ben Yehudah wrote an article arguing for a new approach, one that tied nationalism to the revival of the Hebrew language. The article focused primarily on nationalism and on the Jewish movement for a state, but many have marked its importance (including Ben Yehudah himself) in the revival of Hebrew. Ben Yehudah, you see, is widely considered the father of modern Hebrew, and a controversial figure at that.

Ben Yehudah made it a life mission to revive Hebrew. He resolved to only speak in Hebrew with those who knew the language. He spoke only Hebrew with his wife, and taught his son Hebrew as well (controversial, because his son therefore knew no language with which he could communicate with many others). His son was the first native speaker of Hebrew in over 1,000 years, as a result.

In 1889, Ben Yehudah and 4 colleagues founded the "Safah Berurah" society (translates in Hebrew to "Clear Language"), later renamed "Va'ad Ha-Lashon Ha-Ivri" (Hebrew Language Council, roughly). This Council undertook the work of devising piecemeal an update to the Hebrew language, that would help adapt it to the needs of modern language and schooling. Their goal was to spread knowledge of Hebrew and have it eventually be taught in all schools teaching Jews in the area. Schools that Ben Yehudah spoke to were willing to teach subjects in Hebrew, and by the 1900s, the Teachers Association was founded and resolved to teach in Hebrew as well. The Council had been declining until this point, but got renewed life, and began handing out more vocabulary lists and information to teachers to encourage use of the language. In 1912, the World Zionist Organization began giving financial support and encouragement to the Council and to the Teachers Association to this end, and by 1914, schools all over what became Israel in 1948 were teaching Jewish students Hebrew. This led to the eventual recognition, thanks to Zionist leadership urging, of Hebrew as the third official language by the British Mandate in Palestine.

By 1948, of the roughly 700,000 Jews in what became Israel, Hebrew was the primarily language used by over 500,000. The encouragement, Zionist support, and importance of Hebrew as viewed through the lens of a national movement, had been underway for over 50 years, and the revival and update of the language made significant headway.

To give a bit more information to add on to /u/ghostofherzl's excellent answer, part of what made Hebrew "work" was ideological rejection of the other obvious language choice, Yiddish. Most early Zionist migrants spoke Yiddish. A minority spoke German, which is closely related, and some spoke Slavic languages too. However, soon after Eliezer Ben-Yehuda began reviving Hebrew as a natively-spoken language, the Zionist consensus developed that Yiddish had to be actively rejected as a "diasporic" language, unsuitable to the "new Jews" who would not be under non-Jewish domination. Yiddish reflects Jewish history in Europe, and successive places Jews have called home, which was seen as a big negative. It was the language of the ghetto (in the "where Jews have to live" sense, not the Holocaust sense, since the Holocaust hadn't happened yet at this point). Zionists not only refused to speak Yiddish, they agitated to get others to stop, by protesting and disrupting Yiddish theater and by producing pro-Hebrew propaganda, most famously the slogan עברי דבר עברית "Hebrew, speak Hebrew!".

There was a small Middle Eastern population of Zionist migrants, plus the pre-Zionist Jewish population, who spoke Arabic primarily. When immigrants from the Middle East came in large numbers in the early 50s, the neutrality of Hebrew was an advantage, in that it was the universal Jewish language, not the language of a specific Jewish sub-group. This advantage existed ideologically before Israel existed, but it was a practical benefit afterwards.

It's also worth talking a bit about Hebrew's role in Jewish communities pre-revival. Hebrew was widely used as a liturgical and literary language. While the average person couldn't have a conversation in it easily, people were writing material, borrowing or coining vocabulary for new concepts, etc, and had been for centuries. But it was a somewhat-elite language, for people who had Jewish education (which would exclude most women, and a fair chunk of men, who could read words from a page but might not consistently know what they meant). A lot of Hebrew vocabulary had been borrowed into Jewish vernaculars. While works for laymen would be written in vernacular, Hebrew texts were written for the educated, but not only for the clerical elite. Often vernacular works would be translated into Hebrew so they could circulate more widely in the Jewish world. Its role was similar to that of Latin in Medieval Christendom. This meant that reviving Hebrew was a radical step, it was not a complete break with the linguistic precedent of Jewish communities.