Two main reasons that prompted Europeans to migrate to the United States during the 19th century are:
1) Promise of material affluence
Around 12 million people landed at Ellis Island in New York Harbor for immigration inspection, all with a hope and dream for better living including money and land. Population pressure and fragmentation of rural land, spread of railroads and progressive substitution of sailing boats by steamers were some of the most determining factor that augmented Europeans to migrate to the US. Moreover, "England abolished slavery in 1832, followed by France in 1843 enabling many former slaves to go to the US where laborers were needed".
2) Potential civic freedom
Between 1870 and 1914, America started to symbolize a paradise of freedom in the eyes of members of oppressed nationalities or religious minorities. A new world was being developed and people viewed the US as a place for freedom of religion and new opportunities.
One reason why people moved to North America is because they wanted freedom. There is a high chance that they moved because their country didn't give them enough freedom, like America did.
Another reason why people moved to North America is because of the possession of money and property. They believed there was a high chance of finding a job. They also knew that there was a better chance of getting better land is because America is very large and there were railroads, boats, etc.
I'm assuming you mean why did people immigrate to America from other countries. People immigrated to America for freedom and opportunity.
A lot of countries were in a bad state during the 18-1900s and people heard that America was the "land of opportunity". People came here, and still do I suppose, to live a better life. They would have religious freedom as well as more rights when they moved here. They could find good paying jobs, a good living space for their family, and resources to live happily.