The four great waves of immigration were from the 1600s to the Revolutionary War, the 1820s to the early 1870s, the 1880s to the 1920s, and the last that began in 1965 then accelerated after the passage of the 1991 North American Free Trade Agreement. In the first wave, European wars and religious persecution gave immigrants the push, and the promise of land gave them the pull. The other main cause for immigration during that period was the slave trade, where hundreds of thousands of Africans were kidnapped and forcibly shipped to the region -- especially as the cotton trade expanded. The second wave was driven by a terrible famine in Ireland and German farmers seeking inexpensive land. The third wave was composed of Southern and Eastern Europeans, many southerners from Italy and many Jews from Eastern Europe, where modernization had left many people without livelihoods, and transit tickets on intercontinental ships became widely available.
The fourth wave began in 1965 with changes in immigration laws. Nationally encoded immigration quotas were repealed in the 1965 Immigration and Nationality Act. The act was passed in conjunction with other civil rights legislation, because the "national" quotas were seen as largely a racial quota system. This opened a door that had been closed to many Latin Americans; but there was no real motivation for Latin Americans to leave.
Policy alone did not precipitate the greatest influx of new immigrants, this time from Latin America. The policy worked in conjunction with the North American Free Trade Agreement, passed in 1991, to create the biggest demographic shift in recent history in the United States. With the enactment of NAFTA, however, U.S. agribusiness was allowed to unload massive quantities of cheap, government-subsidized grain -- especially corn -- in Latin America, which undercut Latin American farmers, who then lost enormous amounts of land when they couldn't pay debts. The local economies could not support the influx of landless people into the cities, and Latinos then poured into the United States where they were incorporated into low-paying work.
These great trends account for the historical circumstances that led to the four great immigration pulses, but there are more perennial reasons for immigration that attach to these specific circumstances. The most basic of these reasons are family attachments. Once one member of a family has immigrated, he will miss and be missed by other family members, and they will seek to be reunited -- sometimes by additional immigration. Immigrant families also constitute new social networks in the United States, and these networks create new economic opportunities for family and friends from former communities.