What is the meaning of Simple?

Uncomplicated; lacking complexity; taken by itself, with nothing added.

Easy; not difficult.

Without ornamentation; plain.

Free from duplicity; guileless, innocent, straightforward.

Undistinguished in social condition; of no special rank.

Trivial; insignificant.

Feeble-minded; foolish.

Structurally uncomplicated.

Consisting of one single substance; uncompounded.

Being non-trivial, and admitting no proper non-trivial quotients.

Being non-trivial, and having no proper non-trivial normal subgroups (equivalently, no proper non-trivial quotient groups).
Being non-trivial, and having no proper non-trivial submodules (equivalently, no proper non-trivial quotient modules).
Being non-zero, and having no proper non-zero two-sided ideals (equivalently, no proper non-trivial quotient rings). For commutative rings, this definition coincides with that of a field.
Containing more than one element, and such that the only congruences on the structure are the diagonal relation (the equivalence relation $a\equiv b\iff a=b$ ) and the universal relation (the equivalence relation such that $a\equiv b$ for all $a,b$ ). Equivalently, containing more than one element and having no proper non-trivial quotient algebras.
Being non-isomorphic to the terminal object, and such that its only quotient objects (up to isomorphism) are the terminal object and itself.

Being non-trivial, and having no proper non-trivial normal subgroups (equivalently, no proper non-trivial quotient groups).

Being non-trivial, and having no proper non-trivial submodules (equivalently, no proper non-trivial quotient modules).

Being non-zero, and having no proper non-zero two-sided ideals (equivalently, no proper non-trivial quotient rings). For commutative rings, this definition coincides with that of a field.

Containing more than one element, and such that the only congruences on the structure are the diagonal relation (the equivalence relation $a\equiv b\iff a=b$ ) and the universal relation (the equivalence relation such that $a\equiv b$ for all $a,b$ ). Equivalently, containing more than one element and having no proper non-trivial quotient algebras.

Being non-isomorphic to the terminal object, and such that its only quotient objects (up to isomorphism) are the terminal object and itself.

Being non-abelian and having no proper non-zero ideals. (Note that this is non-equivalent to the usual algebra sense; in particular, the abelian Lie algebra of dimension 1 over any given field is non-trivial and has no proper non-zero ideals, but is by convention not considered simple.)

Equal to a finite linear combination of indicator functions on measurable sets.

Not compound, but possibly lobed.

Using steam only once in its cylinders, in contrast to a compound engine, where steam is used more than once in high-pressure and low-pressure cylinders.

Consisting of a single individual or zooid; not compound.

Homogenous.

Mere; not other than; being only.

A herbal preparation made from one plant, as opposed to something made from more than one plant.

A physician.

A simple or atomic proposition.

Something not mixed or compounded.

A drawloom.

Part of the apparatus for raising the heddles of a drawloom.

A feast which is not a double or a semidouble.

To gather simples, i.e. medicinal herbs.

simple (uncomplicated)