There are a bunch of extra states added. Think Colorado and Wyoming, the two rectangular states just east of the west coast. Now there are 4 rectangular states. Another example: just east of New York and west of Maine are Vermont and New Hampshire. Now there are 3 states instead of 2. It's like that throughout.
Bunch of extra states with similar shapes to existing states, so it messes with your eye and kinda blends in.
Might be harder to do with a map of Africa, Asia, Europe or south America because there aren't as many straight line borders and things are a bit more curvy.
What's interesting are the states you can't modify too much or it gives away the game.
Texas is a key example, people are pretty familiar with that shape, even many non-Americans will recognize it. Florida and California are also pretty well known. Also, many people have a rough idea of NY State, though you could probably tweak the north and west borders a bit and nobody would notice too much.
The ones it's easy to fiddle with are the rectangular ones in the mid-west. I think a lot of people only know them starting from another reference point, like "north of Texas" or "east of Nevada".