They are the width of the shoe. C is the most narrow, D is average, E is wide. Then there are multiple Es also — like EEE — for even wider.
Shoe Size Letters
Shoe Width Letters
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RE:

What do the letters mean after US shoe size, eg 11EE or 11D?
The letters designate the WIDTH of the shoe. Higher the letters, the wider the shoe. EEE is pretty wide, like SASQUATCH foot wide as I remember it (thats the official shoe manufacturers term).
EE is for a very wide foot. D is for regular wide. If regular shoes are a bit too tight for you, D will work fine. If you have problem feet, you might need an EE. You could go to a good shoe store, and just get measured. Or use the link below to go to the website that tells you how to measure your foot and convert to size.
The letters equal the width of the shoe(by the toes). The higher the letter, the wider, EE is wider than D!
They refer to the width of a persons feet in regards to buying shoes. D is average for most men. EE would mean a wide foot compared to somebody who is a D!
The numbers mean the length of the feet, the letters mean their width.
That is how they tell you the width of the shoe is the U.S.

AA would be more narrow, A next, B, C, D, and so on.

EE or EEE would be very wide .