Common examples of symbols are the symbols used on maps to denote places of interest, such as crossed sabres to indicate a battlefield, and the numerals used to represent numbers. Common psychological symbols are the use of a gun to represent a penis or a tunnel to represent a vagina. See: phallic symbol and yonic symbol.
Spoken words are the symbols of mental experience, and written words are the symbols of spoken words.The word "cat", for example, whether spoken or written, is not a literal cat but a sequence of symbols that associates the word with a concept. Hence, the written or spoken word "cat" represents (or stands for) a particular concept formed in the mind.
Another example of the symbol "cat" would be an object, such as a stuffed animal, that is referred to as a cat. The stuffed animal resembles (or exhibits similarity) to a real cat. One can view the object and see the semblance to the real creature that is known to have fur, is soft to the touch, and purrs.
The study or interpretation of symbols is known as symbology, and the study of signs is known as semiotics.
Objects have physical properties; a scepter is essentially a rod with ornamentation. The rod only becomes a symbol of power when people (1) view a scepter held by the hand of a monarch and (2) accept the monarch's authority (or right to use power).
An alien from outer space might describe a royal audience as follows: A Homo sapiens wrapped in fibers reflecting light at the high end of the visible frequency range moved an ornamented rod against gravity, at which time other individuals ceased emitting complex sound waves. A human would say that the monarch dressed in a purple robe waved the scepter to silence the crowd.
What is the difference between these two meanings? Leslie White approached the question in an effort to define cultural objects, such as a law, a constitution, a marriage ceremony. All the nouns in the paragraph above are cultural objects: the monarch, the robe, the scepter, the language, and the subjects.