Europeans started making the journey across the Atlantic in order to expand their influence over world affairs and discover unknown riches. Although the Spanish were among the first Europeans to settle and explore what is now called the United States of America, England became an important power in the settling and colonizing of the land.
Over the course of time, as more and more people began the journey across the ocean, one of the main "selling points" of starting anew in the Colonies was the fact that people were able to come, settle among others who shared similar ideals and views, and ultimately be free to pursue their own religious journey. Remember, life in England was difficult— with religious persecution, civil war, recurrences of the plague, and crop failure due to climactic events of the Little Ice Age.
Making the journey was not an easy choice as there was little infrastructure to support increasing numbers and peoples had to secure land, food, and means for themselves. For many, however, the benefit of being able to pursue their religion and establish a "new life" on an unknown continent, after braving weeks and weeks at sea, was still a better option than remaining in unstable conditions in England.