That "semantic" conception can be seen as articulated in quite different ways, respectively, in Husserl's phenomenological theory of intentionality and in Tarski's metamathematical theory of truth. There are historical links between Husserl and Tarski. But my emphasis here will be on the intuitive...
This chapter succinctly outlines, with headings and sub-headings, Tarski's paper on the establishment of scientific semantics. For each paragraph, it gives the page references for the comparable passages in his truth monograph and in his English-language article "The Semantic Conception of Truth ...