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).