Traditionally, magic involving the elements seeks out the energy of the elements to help empower various other spells and rituals. If you look up the occult meaning of the elements, you'll find more substantial information concerning them.
Fire, for example, purity and warmth. It offers light and passion, which can be taken to extremes.
Water is fluid, and cold. It helps bind all things together, and offers healing. Some say it influences dreams.
Earth is solid and stable. It offers fertility and growth, as well as rigidity, but can sometimes be too rigid.
Air is intangible and whimsical. It is creativity, thought, etc. The phrase lost in the clouds very much applies.
Not exactly the most in-depth explanation of each element, but it should give you the basic idea as to their actual uses within magical practice. They are not used to control tides or create balls of fire. This is fiction.