In the end of the XIX century most Jews were concentrated in the Russian empire.
(Modern Poland, Ukraine, Belorussia). Until 1917 Jews in the Russian empire
were discriminated (Pale of settlement, restrictions on education, discrimination in the army etc.). There were pogroms,
people were killed, their property destroyed. With the start of WW I, conditions for many
Jews became intolerable. So many of them wanted to emigrate. US was a principal destination for several reasons. The main reasons were:
a) religious tolerance,
b) immigration policy which made large scale immigration possible. After all, this is a
"country of immigrants",
c) the reputation of US as "a land of opportunities". In any case, the immigrants find
it easier in the US than in other countries to completely integrate into the society.
Palestine was also a destination for Jewish immigrants, but on a much smaller scale; a Jewish
state in Palestine was only a dream, and neither the Turks before WW I, not the British
after it welcomed immigration. And the local (Arab) population never welcomed immigrants...
The second largest Jewish population was in Austro-Hungary. Conditions in Austro-Hungary
were much better than in the Russian empire, but only until 1914. After WW I,
(and Hungarian revolution) the empire collapsed in several national states,
each with strong nationalist feeling, and nationalist policies.
Many Austro-Hungarian Jews also wanted to emigrate, and US was also
a prime destination.
Several other peoples which felt oppression or lack of opportunity at home had very large immigration to the US
at the same time (Irish, Italians).
Finally, I add that a very large Jewish population still existed in Poland/Ukraine/Belorussia between WW I and WW II. Perhaps more than in the US.
And you know what happened to these people... Most of those who survived, eventually moved
to Israel or USA.
Some numbers. Jewish population of Russian empire (including Poland) according to 1897 census: 5,189,400.
This was slightly more that 1/2 of the total number of Jews in the world.
Jewish population of Soviet Union before WW II was aproximately 2,500,000 (not including
the part of Poland annexed in 1939).
An estimate of the number of Jews who emigrated to the US in 1880-1928: 1.7 million.
Number of Jews in Russia now: 194,000. An estimate of the number of those who emigrated to Israel (after the creation of Israel) - 1 million. Etc. Sources:
EDIT. Exact statistics of immigration to the US is not available because the US authorities
do not ask you about your religion. Which confirms the point a) above.
To address the interesting question in the comment of Andrew Grimm:
34 million people in the US claim Irish descent (12% of population of the US).
Population of Ireland is 6.4 millions. Source: Wikipedia.