Most cultures have specific symbols that are used throughout that culture and understood by its members, such as a dove for peace and fire for destruction. These symbols are not universal, though: symbols depend on context for their meaning.
In writing, we have the privilege of creating our own symbols. These need not be “traditional,” and can even run counter to tradition. We can imbue an ordinary object, such as a piece of chalk, with a deeper meaning by showing the relation between that object and the lives of the characters. These are symbols that are specific to the work, and some authors/artists have symbols that recur across multiple works. Consider, for example, the use of ants by Salvador Dali. Ants occur in multiple works by him, and many (but not all) agree that they are used as a symbol of corruption and decay.
If we use a variety of symbols in a single book and those symbols are linked, we create a motif. It’s common to hear about a “water motif,” for example, in which every sad scene somehow involves water (rain, the ocean, etc.). More unusual motifs can be created as well. By writing them with intention, we can create unusual and memorable works. Few will remember the book with the water motif (unless it stands out in some other way), but unique motifs will imprint themselves on the reader’s mind.