Think of Wiccan correspondences as spell-enhancers. To put this into context, picture your spell as the arrow of your intent that you shoot into the universe toward your target. There are three things that can improve your shot: (1) the physical features such as type of wood and feathers that make up your arrow, (2) your shooting technique, and (3) random environmental conditions such as weather. Wiccan correspondences fall into the first category. They are features that enhance your spell. With the correct enhancers and enough skill in casting a spell, you better the odds that your spell will fly true to its target past the many random obstacles that exist within the universe to block your intent.
Spell-enhancers are things with strong symbolism. They are called correspondences because each has a meaning that corresponds with a purpose of a spell. You just have to choose the correct correspondence to support the type of spell you wish to cast. Take color for example. White symbolizes purity and red stands for passion. You would choose white for your altar cloth and candles for a purification rite, and red for a spell to enhance sexual performance. Think of correspondences as ingredients in a recipe. If you add the right types of correspondences that match the intent of your spell, you improve your spell. Some correspondences such as crystals and colors may act as physical props on your altar to strengthen your focus and increase your belief. Others, such as astrological timing or phases of the moon, go beyond the role of mere equipment and enable us to interact with aspects of the external universe that might have otherwise seemed beyond our control.
Typical correspondences include the following:
Timing: Positions of the stars and planets, days of the week, phases of the moon, time of day or night, and seasons of the year all have a bearing on when you start and conclude a spell and what types of spells you cast during different time periods.
Plants: The meanings of herbs and flowers determine which to use in oils, tea, and incense for which particular type of spell.
Minerals: The symbolism of stones and crystals either worn or displayed upon your altar enhances various types of spells.
Colors: All colors have symbolism, and color is one of the most basic and powerful of all correspondences.
Elements: Earth, fire, water, and air all correspond to certain types of spellwork.
Are you required to use correspondences when casting spells? No. At a minimum, a spell involves willpower and visualization as you raise energy, focus it, and release it to carry the intent of your spell into the universe. But why do the bare minimum when you can give your spell every advantage? Very few witches have the ability to cast a coldly cerebral spell that involves no physical equipment or enhancements, and not many would want to forego the wealth of sensory enhancements that the physical world has to offer. Witchcraft is a tactile art and feels incomplete without correspondences.
Even minimalist Wiccans like me who wish to avoid stockpiling an entire theatre groupís worth of props can benefit from using correspondences of the most ephemeral kind: timing, herbs, and stones to be returned back to nature. The next time you cast a spell, try to include as many correspondences as you can that boost the intent of your spell. Write up your results in your Book of Mirrors and see how you feel about using correspondences to enhance your spells.
One final thing to remember -- the meanings of various correspondences are not absolute. Most new Wiccans learn about correspondences by starting with lists published by renowned experts such as Scott Cunningham, but every Wiccan will eventually develop his or her own feel for what each correspondence means personally to him or her. If you loathe the color green, you may have good reasons for not wanting to use it in a spell to increase your health even though the overall Wiccan culture associates green with vibrancy. As with everything else in Wicca, you start by learning the accepted ways and then you get a feel for your own unique path.
See the CORRESPONDENCES subsection on the Wicca site.
The following books which can be found on Amazon.com may help give you a feel for correspondences: Cunningham's Encyclopedia of Magical Herbs, Cunningham's Encyclopedia of Crystal, Gem & Metal Magic, and The Complete Book of Incense, Oils and Brews.