Where is standard American English derived from?

“Standard” American English (SAE), when used to describe accents, is identical to the term “General American English”, and means American English spoken without any clear regional dialect markers. Sociolinguists tell us that this means essentially English spoken in the north midlands region, like Iowa, but in reality it is spoken all over the country, even in places where many people speak with what others would describe as “heavy” or “thick” accents. SAE is the English used by most television and radio broadcasters—that is, those who don’t speak with an identifiable regional accent.

In truth, a “standard” American accent is defined more by what it isn’t than what it is. It does not have the Northern Cities Vowel Shift, New England non-rhoticity, features of New York English, or any of the phonological features of Southern American English.

There is some debate as to whether speakers with or without the cot-caught merger (that is, whether or not the words cot and caught are pronounced differently) are speaking SAE, but most would consider that not a defining characteristic of SAE.

Some people will point to the Midwest as the location where Standard American English is spoken. But, most dialectology work has found that there is no region without a regional accent (for example see the Atlas of North American English).

For the most part, when your average commentator, or even a linguist, refers to Standard American English, what they mean is "speech which has no salient regional or dialectal markers." That is, Standard American English is largely negatively defined. There is no x such that Standard English sounds like x. Rather there is a, b and c such that Standard English does not sound like a, b or c.

First of all (as an American), I have no idea what "standard American" means--there are distinct regionalisms, but no one of them is "standard." While it's probably not disputed that there's an American dialect (usage, spelling, etc.), there's no "standard" American accent.

Off the top of my head, I can think of a number of regional accents (Northeastern, Southern, Midwestern) that can be broken down further (Texas has an accent that is distinct from a deep Southern accent, even though both can be called "Southern"; Boston is known for its non-rhotic "r" sounds, but the same type of non-rhoticity can be found throughout northern New England).

As other answers have stated, there are distinct markers that identify particular regions that, when none are present, the speaker could be said to be speaking "without an accent".