How did the English colonists that moved to the New World lose their English accents that became what is now American accents. Edit: clarity
It's not clear what you mean by this. First of all, everyone has an accent. If you read through the FAQ section you may find an answer to your question, for instance here: American and British accents.
Current research indicates that in, for instance, the North American colonies around the time of the American Revolution, the colonists largely retained an older pronounciation, but that England's accents began changing very rapidly. In this respect, American English has to some extent retained archaic pronounciation and vocabulary that are sometimes thought to be American inventions, but which are in certain instances elements from an older English. However, American English has always been diverse and it has also changed over time as well.