Proteins are the building blocks of life. They are the structural parts that give cells shape, the enzymes that build or break down the molecules of life, the motors that transport things, the agents that send signals and regulate the activity of other proteins and genes, and the morphogens that help determine the development of the organism.
What determines a protein's activity and properties? Its shape. And what determines its shape? The way its one-dimensional string of amino acids folds together. This is a complex process involving many interactions, so complex that we cannot reliably predict a protein's structure based on its sequence.
To get an idea of the problem, take a look at the picture above, the figure on the left. This is an illustration of a single protein called porin, whose structure has been determined experimentally. This protein has around 300 amino acids. What you see here is the arrangement of all its covalent bonds between atoms, shown as sticks.
Making sense of that tangle of bonds is difficult. So scientists often depict proteins in a simplified cartoon form that shows the secondary structure of the protein fold. These secondary structures are motifs within the protein that form either alpha helical coils or flat beta sheets, and are therefore drawn as coils or flat arrows in cartoon illustrations. The middle picture above shows porin, in the same orientation and size as the picture on the left, but now drawn in cartoon form. Porin is composed mostly of antiparallel beta sheets, arrayed in a barrel-like shape, with an opening in the center.