Grow mediums exist to provide a stable base for your plant to grow its roots through and to hold up the weight of the plant. Over the years many substances have been found to fill this role and they have different properties. Often a grower will use one or more of these mediums depending on the methods he has chosen for growing and the desired properties of the medium in the container being used.
Good old earth. Soil is actually a composite of a number of substances and varies from one location to another. Soil is typically composed of rock, sand, clay, and organics. Organics are decomposed plant and animal matter and provide the nutrient content that is contained in soil, clay binds soil together and retains moisture, rocks and sand provide drainage to allow for root oxygenation. Additionally soil is usually teaming with microorganisms that are feeding on and breaking down the organics contained within it.
If growing a potted plant indoors you will probably want to mix at least perlite with your soil to enhance moisture retention. It is also highly recommended that potting soil be used in a pot rather than soil that you have dug from the ground. A potting mix can be more carefully designed for optimal plant health and the soil outside will contain many unwanted forms of insect life that can and will infect and kill your plants.
Another common concern with soil is that potting soils often already have fertilizers in them (in addition to the nutrients contained in the organics). In general, try to avoid potting soils with time release nutrients but if you do purchase a bag, be aware that the plant will not need any nutrients for a period of time and just water with clean water to avoid burning the roots.
Perlite is a porous white substance that is very absorbant and excellent at retaining and wicking moisture. Perlite is often used for cloning and mixing with other grow mediums but can also be used on its own. Growers who use perlite as a sole grow medium will often purchase large coarse chunks rather than the smaller porous perlite that is more readily available in most areas. It is not recommended to use perlite in a circulating system because the fine dust that comes off the perlite will clog pumps over time. The same fine dust brings a recommendation that when handling perlite you utilize a respirator device so that the dust does not harm your lungs.
Perlite is completely inert substance so will not interfer with your feeding schedules. That said, there are manufacturers such as Miracle Grow that put nutrients in their brand of perlite even though it is not indicated on the label. This material can be used but should be flushed thoroughly with water to wash out the nutrients. Perlite should be washed anyway to remove the fine dust that builds up in it.
Vermiculite is a crushed volcanic rock medium that provides excellent drainage when mixed with other grow mediums. Vermiculite is inert but is not particularly suitable for use as a grow medium by itself.
Rockwool is literally spun rock. Much the way sugar is spun into cotton candy the rock is spun into a material that looks similar to the spun glass used for insulation (but not so itchy). Rockwool is completely inert and most growers are using rockwool in some form. If allowed free drainage rockwool will retain just the right amount of moisture and drain the rest off.
Rockwool comes in multiple sizes of cube. There are smaller cubes or plugs that are typically used for seedlings or clones and larger blocks that are used in hydroponic systems such as ebb and flow trays. Some of the large blocks have holes in them to make it easy to insert the small plugs or cubes you used to clone the plant directly into the larger block
The only concern with rockwool is that it should be completely submerged in water for 8hrs prior to use in order to remove any air bubbles in the medium.
Hydroton is one name for a medium that consists of lava rock or clay pellets that are available in different sizes and usually have a red coating on the outside. This inert medium is effective in continuous drip and ebb and flow systems. It is also an excellent choice anywhere you need drainage and some have used it for the bottom couple of inches of a hempy bucket to facilitate free drainage.
This is a fairly new medium that many are beginning to use. Coconut fiber offers some of the buffering capacity of soil, drains well, retains enough moisture to be useful, and has little nutrient content.