Colorant
Colorant provides the marker with its color and its permanence. Permanent markers come in a variety of colors and that color is provided by a pigment and not a dye. Pigments possess two advantages over dyes. First, they resist fading, thus allowing them to last longer. Secondly, when the marker encounters paper, pigments adhere better and prevent the mark from going through the paper to the other side.
Resin
Resin is the ingredient in permanent markers that acts like glue. It allows the pigment to stick to the paper and become permanent. It is described as a "binder." Resin in markers is the ingredient that adheres to a variety of surfaces -- according to Sharpie -- as permanent markers can be used on more than paper. Urethane acrylic, a resin used in house paints, is a common resin used for permanent markers.
Solvents
The final ingredient in a permanent marker is the solvent, or the substance that mixes everything together. Xylene is one such solvent. Open a permanent marker and experience a bad smell and you have found a marker with xylene. Most markers today use alcohol; so you are less likely to encounter the foul odor. Permanent markers need a solvent or else the marker would not function properly.
How Permanent?
Permanent does not mean forever, at least for a marker. In response to a question, Sharpie does not have a definitive answer to how long permanent marks last. Use indoor and they state the mark from a dye-based marker should last for years on paper or canvas.