The separatists, people who wanted to separate from the Chruch of England, moved to the Netherlands to be free from the Church but didn't want their children to grow up Dutch, so they moved back to England
The separatists bought two different ships, the Mayflower and Speedwell, so they could get to the New World (America) and have religious freedom and be able to practice the English traditions.
The Speedwell set off first but leaked, so it had to be brought back for repairs. Once it was repaired, it set off again but started leaking just 300 feet away from the port, so it turned back again.
The separatists decided not to use the Speedwell and just used the Mayflower. This meant that all the people and cargo of two ships had to fit into one. This made the living quarters very cramped, and many got seasick.
The Mayflower encountered many storms, throwing the ship off course and causing damages to the ship. A beam even cracked during the storms.
The Mayflower eventually landed at Cape Cod, and the Pilgrims settled there, even though their intended location was Virginia.