Signs are signifiers of an object or concept that have an existence in reality.  They stand in place of that object or concept and ultimately represent it.  Most written and spoken signs are symbolic, meaning that the sign has no direction connection to the idea it is representing and is therefore completely arbitrary (Beck et al., 2005).

Example:

This is a picture of a cat.  Because this is not the actual mammal but rather a photograph, the picture is a symbol and refers to the actual four-legged furry animal.  In the same way, the word "cat" is not really a cat; instead it is a sign that represents the house pet.  The choosing of this word was completely arbitrary, for the word "door" could have just as easily come to represent what is now known as a cat.  Yet English speakers have come to agree upon the use of this word, and thus the word "cat" has over time been proven symbolic of the animal.  

See also the definition of symbols.

For more information, read M.A.K. Halliday's article, "Language as Social Semiotic."  The article relates the social system to the linguistic system and determines how people construct meanings from such contexts.