One definition of semiotics can be "the study of signs." Thus, it is important to understand what exactly signs are and the different types of signs. Chapter 2 in Semiotics and Communication: Signs, Codes, and Cultures by Wendy Leeds-Hurwitz discusses signs and some of the key terms associated with them.
A sign is defined as "everything that, on the grounds of a previously established social convention, can be taken as something standing for something else." Examples of signs will come later. First, let us look at the two main interpretations of signs -- dichotomy and trichotomy.
Dichotomy is a two-part relationship first outlined by Swiss linguist Ferdinand de Saussure. Saussure split each sign into two parts: the signifier and the signified. The signifier is the visible or explicit part of the sign; the signified is the invisible, implicit part of the sign. Take a wedding ring, for example. The signifier would be the wedding ring itself. The signified would be the marriage between the man and the woman. Saussure's dichotomy is probably one of the most widely recognized theories in semiotics.
Trichotomy is a three-part system created by ------- Peirce. It is similar to Saussure's theory, but slightly different. The three parts to the trichotomy are the representatum, the object and the interpretant (the representatum is also called the sign. I will use the term representatum to avoid confusion). The representatum is the same as Saussure's signifier, but Peirce split the signified into two more specific parts. The object is what the representatum refers to; the interpretant stands for the meaning conveyed by the representatum about the object that was not previously known but here conveyed. Let us use the wedding ring example again. Here, the representatum would be the ring itself. The object would be the marriage between the husband and the wife, and the interpretant might be the love they felt for each other during their honeymoon, or perhaps the accomplishment that the man felt when he had saved enough money to buy his fiancee her ring.
In addition, semioticians have classified signs into three separate categories: icon, index and symbol. These categories focus on the relationship between the signifier and the signified. As Leeds-Hurwitz points out, an icon is a sign that has a similarity or resemblance to an event or thing. An index is a sign that is a small piece of a greater whole. A symbol is a sign that conveys an arbitrary or abstract relationship to something. Thake a college party, for example. A picture of yourself and your roommates with your arms around each other holding up cups of keg beer would be an icon since the photo the group of you. An empty keg cup would be an index; it was a small piece of the actual event. The empty keg could be a symbol of the good time (or not-so-good time) you had at the party for the keg is arbitrary and does not actually resemble the time you had.
Aside from specific categories, understanding signs means understanding some specific terms about signs: motivation, convention, connotation and denotation. Motivation (or constraint) refes to "the degree to which the signified determines the signifier." If the signified and the signifier have a high degree of connection, they are considered highly motivated (or highly constrained). An example would be a Polaroid picture since the picture closely represents the actual person. On the other hand, a caricature might be an example of having low motivation; the distorted and exaggerated features of the picture might not accurately represent the person at all.
Convention is a term that refers to "the degree of tradition" that a particular sign has. For example, the colors blue and pink are associated to newborn babies. Although this has been a long-standing tradition, it does not necessarily mean that all baby boys wear blue and all baby girls wear pink. It is simply a tradition that has been passed through the years. Denotation stands for the obvious, straightforward meaning of a sign, while connotation refers to the implicit, second meaning of a sign. A large Thanksgiving dinner most obviously denotes food that is about to be eaten. However, the dinner can connote such things as the time put in by Mom or Grandma cooking the meal, the family tradition of the meal, or the "wonderful" time you are about to spent with Aunt Nellie or Cousin Tex.
If the terminology of semiotics does not confuse the average person, perhaps the argument between the terms sign and symbol might. Over the years, many semioticians and comunication theorists have used the two terms intechangably. However, as mentioned before, a symbol is a specific type of sign, but usually the type of sign that most scholars study. The technical definitions list a sign as "a general category" and a symbol as "one particular variety of sign." In other words, a sign becomes a symbol when it is placed into a certain context. An egg, for example, can be a sign for many things, but when placed into the context of holidays, it becomes a symbol for Easter. Therefore, although they are slightly different in meaning, they cannot exist without each other. A sign must be a symbol in order for it to be a sign at all.
Leeds-Hurwitz's book on semiotics is a great reference for someone interested in the area. Although there is a considerable amount of terminology, she provides many examples for the reader to understand.