Initial raids to Americas by Britain supported by religious rivalry with Catholic Spain. Many settlers migrated to the Americas were also parts of religious minorities like the Puritans who wanted greater freedom than they could have in England.
Navigation Acts passed that contributed to colonists' anger at Britain as they benefitted Britain by saying that the American colonies could only import and export goods with his own ports. This restricted the amount of goods the colonists could access
In 1774, 58 representatives of the colonies meet in Philadelphia to decide what to do next to resist Britain. They declare these colonies independent of Britain in the "Declaration of Independence".
In 1783, the British are militarily defeated in N America after their main general Cornwallis and his army are forced to surrender at Yorktown. The war officially ends with signing of the Treaty of Paris.
The superior weapons (muskets and cannons) of the British settlers allowed them to easily conquer and defeat the Native Americans and clear them off their land.
There was cheap and abundant land in the USA that attracted British colonists who came from a country where land was in short supply. Growing plantations goods like tobacco and cotton and trading them with Britain allowed settlers to make a living.
One of the major motivations for British settlers to migrate to America was religious persecution. Groups like the Quakers and Puritans had greater religious freedoms in the colonies.
The democratic constitutions in the American colonies attracted persecuted groups from Britain. Difference over how the colonies should be run and what their relations with Britain should be eventually led to conflict between the colonists and the British government
The greater freedom and Independence of the British colonists fed the growth of democratic and Republican ideas (rule without a King). These eventually inspired the American Revolution.
Short-term: The colonisation of America created an escape route for religious minorities escaping from Britain. 20,000 moved just in the period 1629-40. The colonization of North American had severe and negative consequences for the Native Americans. Between 1500 and 1700 their population halved as a result of disease, war and famine.
Long-term: After the loss of America Britain focused on colonising other areas such as Canada, Africa and India. By 1900 the British Empire controlled 25% of the world. Britain needed a new colony to send its convicts to after the the loss of America, and decided upon Australia. Australia and New Zealand then became a major destination for emigrants who created goods like wool to trade with Britain. The loss of North America by the British in the American Revolution was costly. 30,000 British sailors and soldiers died and it cost £80 million. After independence the USA became a Republic and developed as it wished. It expanded rapidly westwards from the original 13 colonies to become the USA we recognise today.
King Louis XIV tears up Edict of Nantes and declared Huguenots heretics. Faced with being killed or forced to convert 200,000 Huguenots flee from France