Flat is an attribute that can be assigned to a symbol f to indicate that all expressions involving nested functions f should be flattened out. This property is accounted for in pattern matching.
Flat corresponds to the mathematical property of associativity.
For a symbol f with attribute Flat, f[f[a, b], f[c]] is automatically reduced to f[a, b, c].
Functions like Plus, Times and Dot are Flat.
For a Flat function f, the variables x and y in the pattern f[x_, y_] can correspond to any sequence of arguments.
The Flat attribute must be assigned before defining any values for a Flat function.
See The Mathematica Book: Section 2.3.7 and Section 2.5.3.
See also: Orderless, OneIdentity.