As you already know, semantics is concerned with the meaning of words and sentences we produce (whether in speaking, writing, interpreting them or listening to them).
What do they mean and more importantly, why do they mean anything to us? How come that we more or less agree on the meaning of the word table and why is it fruitless to make up new words for bread such as methilope or methyla or laphina as Ali G did in his interview with Noam Chomsky?
Let me start off with what it means to look at semantics from a cognitive linguistics point of view. Then, I'd like to concentrate on answering the question of how we create meaning; or more precisely the connection between sounds, symbols and meaning.
Until some thirty years ago, linguists that investigated the connection of words and their meaning, claimed that most of the words stored in our mental lexicon were connected to actual things in the objective external world (truth-conditional semantics). Words and their meaning were investigated within the subfield of lexical semantics and were claimed to be stored in our mind by means of definitions; basically indicating that our mind functions like a dictionary. Sentence semanticists would then look at how words in combination would make up a certain meaning, the assumption here being that sentence meaning is composed from word meaning, together with the structure imposed on those words by the grammar. Semantics in the formal approaches to linguistics was, and still is, perceived as being separable from pragmatics, the study of language in use. 'Meaning' according to this view, is encoded in words, regardless of their context of use.
Cognitive linguists, as you can imagine, take a somewhat different approach. First of all, words and sentences do not simply become meaningful by imprinting some sort of definition (in relation to an objective world) into our minds. Instead, things become meaningful to us because of the way our body interacts with the world. Not the entire external - so called objective world - is meaningful to us, but only the things we can perceive and only these will be conceptualized in our minds as form-meaning-pairings. Embodiment therefore determines to some extent the nature of concepts that human beings are able to come up with, or in other words we can say, that conceptual structure is embodied.