The word symbol derives from the Greek verb symballein, to throw together and it noun symbolon, "mark," or "sign." It is an object, animate or inanimate, that stands for or points to a reality beyond itself. The cross, for example, is often used to represent suffering. Symbols, however, also indicate their own reality. For example, a cross not only stands for suffering, but it also stands for Christian suffering. A sunrise not only represents new beginnings but the beginning of a new day. The more you read and study literature, the more you will come across words that always function symbolically. The seasons are a perfect example. Winter represents aging, decay, and death; spring is often used to represent energy, birth, and hope; summer is symbolic of childhood, fun, and laughter; autumn stands for maturity, wisdom, and fulfillment.
Other typical examples include the scales to symbolize justice; a dove for peace, the rose, purity; the stars and stripes, America; the lion, strength and courage, and so on.
Things get a little harder, though, when a poet creates a new symbol. You then have to study the poem carefully and ask yourself which word has a central place in the poem or which word transforms other elements in the poem. The albatross in Coleridge's Rime of the Ancient Mariner is a case in point. The albatross is a recurring character, and it symbolizes the suffering that the mariner is going through.
Sometimes symbols can be straightforward, but more often it is not easy to say exactly what they symbolize. In Blake's "The Tyger," for instance, the tiger could be a symbol of great energy and creativity, but it could also mean many other things. The same applies to Coleridge's albatross. You can guess at the meaning but can never be quite sure. Always remember when discussing symbols and symbolism in poetry that they are rich and complex and have many layers of meaning. Rather than using the words "stands for" or "points to" when you discuss them, try to use words like "suggests" or "expresses" or "represents."