Why are there only the Democratic party and the Republican party currently in the US?

I was looking at the history of the political parties, and I found out that John Adams was a member of the Federalist party, while his son John Quincy Adams was a member of Thomas Jefferson's Democratic-Republican party and then switched to the National Republican party. Andrew Jackson was the first President of the Democratic party. William Henry Harrison, the first President to die in office, belonged to a party called the Whig party. The Whig party was later replaced by the Republican party. Abraham Lincoln was originally a member of the Republican party and then he switched to a temporary party called the National Union party. Andrew Johnson continued with the National Union party after Lincoln's assassination, and then switched to the Democratic party.

My question here is: What is the history behind this evolution?