In linguistics, meaning is the information or concepts that a sender intends to convey, or does convey, in communication with a receiver.
Semiotics
Ferdinand de Saussure in founding semiology, his original subset of the semiotics, started describing language in terms of Signs, dividing those signs in turn into signifieds and signifiers. The signifier is the perceptive side of a sign, thus the sound form in case of oral language. The signified is the signification (semantic) side, the mental construction or image associated with the sound, by either a speaker and hearer. A sign, then, is essentially a relationship between signified and signifier.
Signs are essentially conventional, as any foreign language student is well aware: there is no reason that bat couldn't mean "body of water" or even "that bust of Napoleon over there". Since the choice of signifiers is ultimately arbitrary, the meaning cannot somehow be in the signifier. Saussure instead defers meaning to the sign itself: meaning is ultimately the same thing as the sign, and meaning means that relationship is between signified and signifier. All meaning is both within us and communal, thus cultural. Signs "mean" by reference to our internal lexicon and grammar, and despite there being a matter of convention, so the communal part, signs also, because of the individual's uniqueness, can mean something only to the individual (what red means to one person may not be what red means to another, either in absolute value, or by including what's suggested by the context). However, while meanings carried by one given set of signifiers may vary to some extent from individual to individual, only those meanings that stay within a boundary are seen by other speakers of the language to belong to the language: if one were to refer to smells as red, most other speakers would assume the person is talking nonsense (although statements like this are common among people who experience synesthesia, or in poetry).