The elements of art are sort of like atoms in that both serve as "building blocks." You know that atoms combine and form other things, right? Sometimes they'll casually make a simple molecule, as when hydrogen and oxygen form water (H2O). If hydrogen and oxygen take a more aggressive career path and bring carbon along as a co-worker, together they might form something more complex, like a molecule of sucrose (C12H22O11).
A similar activity happens when the elements of art are combined. Instead of hydrogen, oxygen, carbon, etc., in art you've got line, shape, form, space, texture, value and color. Artists manipulate these elements, mix them in with principles of design and compose a piece of art. Not every work has every last one of these elements contained within it, but there are always at least two present.
For example, a sculptor, by default, has to have both form and space in a sculpture, because these elements are three-dimensional. They can also be made to appear in two-dimensional works through the use of perspective and shading.
Art would be sunk without line, sometimes known as "a moving point." While line isn't something found in nature, it is absolutely essential as a concept to depicting objects and symbols, and defining shapes.
Texture is another element, like form or space, that can be real (run your fingers over an Oriental rug, or hold an unglazed pot), created (think of van Gogh's lumpy, impasto-ed canvases) or implied (through clever use of shading).
Now, I will try not to leap up and down and pinwheel my arms in large, excited arcs over color, but, really - it's often the whole point for us visual types. Show me a red spectrum, regardless of value (lightness or darkness), and my brain yells "Hallelujah!" Then, of course, there are all of those lovely, soothing blues...oh! And green! The color of nature and the renewal of life. There have got to be at least 84,000 tints and tones of green. And, yellow! My goodness, I do love a sunny yellow. Not a sickly-looking "Whoa! Hey, you should get your liver function tested, buddy" shade of yellow, mind you, but...what? Sorry. What was the other part of the question?
Why are the elements of art important?
Right. The elements of art are important for several reasons. First, and most importantly, a person can't create art without utilizing at least a few of them. No elements, no art, end of story. And we wouldn't even be talking about any of this, would we?
Secondly, knowing what the elements of art are enables us to (1) describe what an artist has done, (2) analyze what is going on in a particular piece and (3) communicate our thoughts and findings using a common language.
Musicians can talk about the key of "A," and they all know it means "a pitch relating to 440 oscillations per second of vibration." Mathematicians may use the very basic word "algorithm" and feel confident that most people know they mean "a step-by-step procedure for carrying out computation." Botanists world-wide will employ the name "rosa rugosa," rather than the much longer "that old-fashioned shrub rose - you know, the one that leaves hips in the fall - with the five-petaled flowers that can be yellow, white, red or pink." These are all specific examples of a common language coming in handy for intelligent (and shortened) discourse.
So it is with the elements of art. Once you know what the elements are, you can trot them out, time after time, and never put a wrong foot forward in the Art World.
Does your instructor want you to write a few words and/or pages on a painting of your choice? Choose wisely, and then wax euphoric on form, lines and color.
Have you found an unidentified work in your great-aunt's attic/toolshed/outhouse? It is helpful, when describing the piece to someone who may be able to supply you with further information, to throw in some of the piece's elements of art along with: "It's an etching. It's on paper."
Stumped for conversation at a gallery show? Try "The artist's use of _________(insert element here) is interesting." This is a much safer course than attempting to psychoanalyze the artist (after all, you may be standing in a clump of people that includes his or her mother) or using words which leave you a bit uncertain of exact meanings and/or pronunciations.
See? The elements of art are both fun and useful. Remember: line, shape, form, space, texture, value and color. Knowing these elements will allow you to analyze, appreciate, write and chat about art, as well as being of help should you create art yourself.