In the latter half of the nineteenth century, tens of millions of people immigrated to the United States, mostly from Europe. As your question suggests, this left an indelible mark on the cultural, political, and economic landscape of the country. Early in this period, the majority of immigrants to the United States came from the British Isles, Ireland, the Netherlands, and Germany.
By the end of the century, patterns shifted, with the bulk of immigrants coming from Eastern and Southern Europe. Unlike previous immigrants, who tended to be Protestant (with the notable exception of many of the Irish immigrants), many of these new arrivals were Catholic and Jewish. Furthermore, since many of these new immigrants were from regions that had not provided many Americans previously, they greatly increased the diversity of the country. At times, this led to strife between long-established communities and the immigrants.
This was also a time of urbanization. The majority of immigrants during this period settled in cities, where they typically found employment as unskilled laborers. With so many new factory workers, the country's economic sector expanded. Unfortunately, working conditions and urban housing were often unsafe and unsanitary. These conditions helped give rise to the Progressive Movement of the early twentieth century as workers became more active in politics and social movements.