Settlers came to North America for a variety of reasons. Early European settlers from France, Spain and England arrived for economic opportunity. In most southern European states, inheritance of land and resources went to the first son exclusively. This left many younger men without land and money. In feudal society, it was extremely difficult to make a living for one's self without the family inheritance, so many of these men decided to settle in America.
Some communities, such as the Puritans, settled for religious reasons. The Puritans sought a theocracy in which to govern themselves based on religious law and custom. Since this couldn't be accomplished in Anglican Britain, many decided to settle in the New World.
In coming to the Americas, settlers believed that they would improve their material well-being, gain religious freedom, and form new identities for themselves and their families.
In the beginning, Europeans wanted to find a shorter trade route to India and China and sent explorers westward. They eventually discovered North and South America and found the two continents were laden with treasures. They reported their findings and the push to claim land and exploit its riches began. In the exploitation, the Native Americans were killed or driven off. So the first colonizers came for wealth, then for relocation of prisoners, then for religious freedom. Eventually, the poor and oppressed heard about the "New Land" and wanted to come here. At the height of immigration, boatload after boatload of immigrants came over, all looking for new homes.
How exciting it must have been for those first settlers. America was an beautiful place, new and fresh and exciting. There were streams, forests, and game aplenty. The land was vast, the soil rich. Here they could farm, raise animals, grow gardens and crops, and worship God how they pleased. Many of them learned to live and work with the Indians and take care of the land and animals.
While explorers and early colonizers came to exploit and get rich, the majority of colonizers who came to America saw the possibility of a new way of life, a better life, a fresh start.