In (1892), Frege published his article "Über Sinn und Bedeutung", in which he tries to get through his perplexity about the fact that linguistic expressions habe not only an extension (reference), but also a meaning (intension). Originally, Frege was dealing with, and aware of, the extension of terms, what they 'designate' (German, "bezeichnen"; cf. Frege 1892, 26). But then he became aware that sentences like "The morning star is [the same object as] the evening star" which, if expressions had only an extension and nothing else, would have to be logically trivial--which they in fact are not. To explain the fact that such sentences can be non-trivial, it is necessary to take notice of another aspect of the semantics of terms, namely, their meaning (intension).

As it happened, at that earlier time, at which Frege had not yet noticed that second semantic dimension, he apparently had accustomed himself to the use of the word "Bedeutung" for what an expression refers to, its extension; i.e., he was accustomed to the use of Bedeutung" ('meaning') as interchangeable with "bezeichnen" ('signify'). Accordingly, he was unable to use that term for the second dimension, meaning. Therefore, he had to introduce another term for this. He chose the word "Sinn" ("sense"). According to Frege's terminology, then, the meaning (intension) of an expression is called its "Sinn", while the reference (extension) of an expression is called its "Bedeutung".

There is a problem with this terminology, however. While the word "Bezeichnung" does apply to what an expression refers to, the word "Bedeutung" does not. As a matter of fact, German language does not enable the use of "Bedeutung" for the reference (extension) of a term; "Bedeutung" really applies to an expression's meaning. Frege's definition of "Bedeutung" is inadequate.

Incidentally, notice that Frege does not represent the meaning of an expression as an extension. What he actually does is:

(1) He represents the "Sinn" of an expression as an intension, referring by "Sinn" to an expressions meaning. He thus represents the meaning of an expression as an intension.

(2) He represents the reference of an expression as that expression's extension. To refer to what the expression refers to, Frege uses the term "Bedeutung". 

That Frege uses the term "Bedeutung" for what an expression refers to, rather than for what it means, is rather confusing; because, to repeat, outside Frege's idiosynkratic terminology "Bedeutung" applies to the meaning of an expression.

Since Frege's definition of the term "Bedeutung" does not correspond to the established usage of this word, it amounts to a re-definition of that term. The re-definition of a central term, we said elsewhere[LINK], tends to cause ambiguity of that term. And this is exactly what happened in the case of "Bedeutung". "Über Sinn and Bedeutung" had tremendous impact on the meaning-theoretical debate. Along with this impact, Frege's idiosyncratic usage of the term "Bedeutung" was adopted and became widely established. From now on, within the meaning-theoretical debate the term "Bedeutung" had become ambiguous. Some applied it to meaning (intension), some to reference (extension).

The ambiguity of the term "Bedeutung", in turn, lead to a most serious interpratory mistake: It engendered the view that Frege defends an 'extensional' theory of meaning, in the sense of a theory which identifies the meaning of an expression with its reference. To repeat, for the meaning of an expression, Frege uses the term "Sinn"; and his view of the "Sinn" is common-or-garden intensional. Frege never defended an 'extensional' conception of meaning.

However, this interpretatory mistake, in turn, started its own long and rich life. For decades, and until very recently, philosophers of language used to discuss an 'extensional', 'Fregean' theory of meaning according to which the meaning of an expression is what it refers to, an extension. One prominent philosopher who succumbs to this mistake is Donald Davidson, in his article "meaning and Truth" (1967). There, he tells a long rigmarole of how a certain approach to meaning fails which views the extension of an expression as its meaning--a theory which he explicitly traces back to Frege. This discussion makes up almost the complete space devoted by Davidson to alternative theories, before he introduces his own view; but it is the discussion of a view which Frege never took, of a theory, which is quite obviously beside the point, is not a theory of meaning at all. Click here for more details.