Jurgis wants to marry Ona, but he is poor and after her father dies, Ona's family also ends up poor. Jurgis hears that life is good in America, for Ona's brother Jonas tells him that a friend has gotten rich in the States. Further, Jurgis hears that in America, young men are not forced to serve in the army, that people don't have to pay bribes to corrupt officials, and that workers can earn three roubles a day, which is a fortune in Lithuania. He believes he can go to America and become a wealthy man. So he and Ona and other family members decide to save their money and leave. For Jurgis, this is a way to afford to marry, which he wants very much to do, and he dreams of a better life. Jurgis is willing to work hard for a better future.

Lithuania, as the novel depicts it, is a cruel and exploitative country, and it is easy to understand why these characters would want to leave. However, they also have a false idea of what living in America will be like and don't understand how hard, in reality, it will be to survive.  

In a nutshell, they immigrate to have a better life.  While in Lithuania, they experienced some major financial difficulties.  A friend of the family tells them about all the opportunites in America so they decide to go.  In Lithuania, Jurgis and Ona did not have enough money to marry, but they thought they would be able to have all they wanted, including money to marry, when they moved to America.

Why did Jurgis and Ona's family decide to go to America?

Essentially, the promise that America held for immigrants like Jurgis and Ona was the reason they decide to come to "the land of opportunity."  Jurgis and Ona recognize that their life in rural Lithuania holds little in way of economic or social promise.  Jurgis is animated by the idea of starting a new life with Ona in the new world.  Through she is devoted to her family, Ona recognizes the promise and possibility of a new life, in both economic and personal terms, through coming to America.  For both Jurgis and Ona, this dream of equality of opportunity is what drives him:  

In (America), rich or poor, a man was free, it was said; he did not have to go into the army, he did not have to pay out his money to public officials,—he might do as he pleased, and count himself as good as any other men. So America was a place of which lovers and young people dreamed.

The combination of the mythological promise of America and the idea of being able to live together as young lovers seeking to "make it big," is what drives both of them to come to America.  In this, a vision of the American Dream is conceived.  Through this, the proverbial American nightmare takes hold.