It has a lot to do with the changes in Russia after the assassination of Czar Alexander II and the rise of anti-Semitic wave under Alexander III and Nicholas II.
The entire immigration from the Russian Empire in 1880-1910 years accounted about 2.5 million people. It was almost pure Jewish immigration - more then 80% immigrants were Jews. Before 1880 among all immigrants from Russian Empire the percent of Jewish people was to less then 10%, and after 1910 this percent fell to around 30%. At that time huge Russian Empire is included Poland, Finland, Lithuania, Latvia etc.
In answer to the question of why there was such mass Jewish emigration from the Russian Empire at this particular time, allow me to point out in the shortest possible way, a few historic highlights about Russian Empire.
b> Czar Alexander II had instituted many reforms regarding the Jews, not the least of which was reforming the conscription laws concerning Jews. His purpose had been to try to find a way to get the Jews more assimilated into Russian society.
But he was assassinated in 1 March 1881 and the Jews became the nation's scapegoat.
Official pogroms began to be initiated under Alexander III. In the course of one year, 160 places in Southern Russia went up in flames. In Demiovka, a suburb of Kiev, numerous Jews were beaten to death or thrown into the flames and many women were raped. Jews were maimed and killed indiscriminantly. That caused panic among the Jewish population and they fled the pogroms. There were additional government sanctions which added to the panic. When the Kiev pogrom was tried in a military court, the public prosecutor argued that the pogrom had been brought on by the "exploitation by the Jews" who had obtained the principal economic positions in the province. In addition, the public prosecutor was reported in a Jewish weekly publication as having said, "The Western frontier is open for the Jews..." and that their emigration in no way would be hampered.
Although the pogroms were brought to a stop by world pressure put upon the Czar, the "May Laws" were next enacted. These laws has b> limited settlement of the Jews, sale of property to and by Jews, changed their legal status and resulted in wholesale expulsion of the Jews from their former homes inside the Pale.
According to one historical Russian writer, Czar said that the Russian Jewish question would be solved ultimately by the action of the May Laws "as these would force 1/3 of the Jews to emigrate; 1/3 more would become converted to the Orthodox Church; while the other 1/3 would perish of hunger". Even it that statement were not true, the emotion expressed is exactly what the Jews were feeling. Anyway, the noose was closed even tighter by the enactment of laws limiting the Jews who were allowed into high schools and universities. Then came the expulsion of Jews from St.Petersburg, Moscow and other large cities.
The end result of all this was mass immigration of the Jews, ultimately to the USA for the most part.
As far as when the flood of Jews began to slow down, the citizens of the US were becoming increasingly alarmed at the number of poor, dirty new immigrants and the Congress of the US began to pass laws limiting the number of people who could enter into the US. I believe that by 1910th, such strict laws had been passed that fewer and fewer Jews (and others) were able to come to the US. At this time, large numbers of Jews go to South America and South Africa, which still welcomed them. For them anyplace was better than Russia!