In his "Course in General Linguistics," (which was compiled by his students) Saussure names the science of what constitutes signs and the laws that govern them as semiology. Since semiology deals with signs, it covers psychology, sociology, and linguistics. Saussure believed that to inform each of these applications of semiology, one had to focus on the structure of signs.
The linguistic sign is made up of a concept and a sound-image. The concept is the abstract idea of, say, a tree. The sound-image is the psychological sensory impression of the sound of a word; as sound-image, Saussure denotes a kind of mental impression which is an sound and sight based. In other words, the sound-image is the sense we get when seeing, hearing or saying a word.
Saussure then describes the sign (previously as concept/sound-image) as signified/signifier in order to be more descriptive. The bond between signified/signifier is arbitrary. The signified concept (tree) is represented by the signifier, the word "tree." A community decides to call it a "tree" so they have a common word to which they all can refer. But as there are many languages, the concept can be expressed in any number of ways: Baum (German), Arbor (Latin). So, it is not the relationship between signified (tree) and signfier (word "tree") that gives that word meaning.
However, language does depend upon this link between thought (concepts or signifieds) and sound (sound-images or signifiers).
There is the linguistic sign (signified/signifier) (tree concept/"tree"). That is how signification works. But the meaning of "tree" (Saussure uses the word "value" as "meaning") depends on the context of the word; not the link between "tree" and its signified concept.
A tree is a plant that grows in the forest. I know what a tree is from the context of this sentence. If I write, "A balloon is a plant that grows in the forest" I might think that the word "balloon" means the concept of tree. Therefore, the meaning (value) of a word is not established by the word itself or the bond between word and concept. Rather, the meaning is established between that word and other words; between the signifier and other signifiers.
We can isolate the word "tree" in the context of that sentence because "tree" is different from the other words or signifiers. This seems so basic but it must be mentioned. It is necessary that words (in sound or writing) are different and can be distinguished from each other.
Everything that has been said up to this point boils down to this: in language there are only differences.
We understand "tree" based on its difference from (and relation to) other words in the context of a sentence, story, language, etc. In any context, words are written/spoken linearly: one after another. We don't typically write or say words on top of each other! Two of more words stated linearly (a phrase, sentence, etc.) is a syntagm. I understand "tree" based on the context and syntax (syntagm) of the sentence. But I also think of things associated with "tree" such as nature, carbon dioxide, leaves, branching metaphors, etc. So, the meaning derives from syntagmatic relations (the linear structure of the context and syntax) as well as associative relations.