Algebraics represents the domain of algebraic numbers, as in x Algebraics.
Algebraic numbers are defined to be numbers that solve polynomial equations with rational coefficients.
x Algebraics evaluates immediately only for quantities x that are explicitly constructed from rational numbers, radicals and Root objects, or are known to be transcendental.
Simplify[expr Algebraics] can be used to try to determine whether an expression corresponds to an algebraic number.
Algebraics is output in TraditionalForm as .
See The Mathematica Book: Section 3.3.10.
See also: Element, Simplify, Integers, Root, Extension, Reals.