Gottlob Frege's influential theory of meaning, the theory of sense (Sinn) and reference (Bedeutung), was explained in this seminal work. Frege, at the outset of the essay, says that identity “gives rise to challenging questions which are not altogether easy to answer.” The puzzle raised by identity sentences is that, if, even though “the morning star” and “the evening star” have the same reference — the planet Venus — the sentences
[1] The morning star is the morning star. (a=a, a priori)
[2] The morning star is the evening star. (a=b, a posteriori)
seem quite different. They seem, as Frege says, to differ in “cognitive value.” The first appears to be a trivial case of the law of self-identity, knowable a priori, while the second seems to be something that was discovered a posteriori by astronomers. However, if “the morning star” means the same thing as “the evening star”, then the two statements themselves would also seem to have the same meaning, both involving a thing’s relation of identity to itself. It then becomes too difficult to explain why (2) seems informative while (1) does not. It seems that names in identity sentences neither stand for themselves nor (merely) stand for objects. Then how are names functioning here? Frege’s thought here is: names must have some property, other than their reference, which explains these facts about cognitive significance. This property is their sense. Sense is what explains the difference in cognitive value between [1] and [2]. While the truth of an identity statement involves only the reference, the informativity of such statements involves additionally the way in which those references are determined, i.e. the senses of the component expressions.
In between he goes on about a lot stuff, but his essay is primarily about the distinction between sense and reference, with a special emphasis on the interpretation of the nature of senses which also makes Frege a forerunner to what has since come to be known as the “descriptivist” theory of meaning and reference in the philosophy of language. His approach to language is also symptomatic of the grand ambition of the positivists to create a language that isn't only grammatically meaningful but also logically sane; needless to say, this fell flat on its face.