Many scholars have studied the symbols of Buddhism and here, I intend on tapping on their knowledge to explain some concepts and their importance in the philosophy and theology of Buddhism symbol.
What is a Buddhist symbol? It's simply an image, an object or a concrete representation of an idea, a concept or other abstractions.
Symbols are often cultural or regional. For example, in North America, a red octagon is the symbol for STOP. It is not so everywhere. In Japan, for example, the symbol for it is a red triangle pointing upward. A North-American not paying attention could think that this symbol means "yield" as it is similar to the symbol for such a message in North America.The point I want to make here is that some symbols in Buddhism might seem very odd for Christians but they have to be taken in their context.
A fundamentalist Christian friend of mine was convinced that Buddhists were the Devil worshipers after visiting a Buddhist Mongolian temple. Inside she was confronted with images representing hell and demons. She swore never to enter a Buddhist temple again.
A common misconception is also the use of the famous swastika in Japan. You'll have to read about it to know why.
Some Buddhist deities (like Fudo Myo-o) look like demons but they are actually symbols representing a destroyer of one's own greed-anger-and-ignorance so that one can serve the cause of all living beings.
Mandalas are a tool used by esoteric (or tantric) Buddhist to meditate. There are also different tools and many art form that add content to our vast field of symbols.Many symbols are not connected to Buddhism but some are also used across a number of cultures around the world.