The relationships that can exist between signs can be either syntagmatic or associative. An associative relationship means a relationship between a group of signs, while a syntagmatic relationship means a relationship that exists between signs that are grouped together based on their syntactical meaning. For example, the words "house" and "home" have an associative relationship, while the words "open" and "house" could be said to have a syntagmatic relationship.

According to Dictionary.com, the definition of "house" is "a building in which people live; residence for human beings," while the definition for "home" is "a house, apartment, or other shelter that is the usual residence of a person, family, or household." Almost immediately one can see how it is the relationship between signs that creates meaning, because Dictionary.com actually uses "house" in its definition of "home." The two are clearly related via an associative relationship, but it is their difference that actually...

A house is the physical object on its own, but a home is that physical object considered in specific relation to an individual. This example helps demonstrate how the system of signs ultimately determines a sign's value as well as what Saussure means by associate relationships.
Saussure's contributions to linguistics are important precisely because they help one separate out the underlying elements of language beyond what is apparent. Usually people imagine words as discrete, independent objects whose meaning is inherent, but Saussure demonstrate that words are actually merely one element of the more complex notion of the sign. By applying Saussure's theory to signs, one is able to see how it is the interplay between different signs that allow human beings to create meaning and use language to express it.

References

Saussure, F. (2011), Course in General Linguistics, Columbia University Press, New York.