I almost wrote that soilless potting mixes and soilless media in general are great for small-scale gardeners when I suddenly recalled that a Hungarian farmer is using soilless media to grow pepper and tomato on 5-6 hectares (and using thermal water for irrigation, so the whole cycle is absolutely sustainable).

Anyway, back to mixes: the generally have the following components:

• Peat moss: used for improving aeration, drainage and water retention, so the medium does not dry out too soon. Downsides are that it is difficult to to wet, so you have to moisten it before adding to the medium. As pointed by fellow Quorans, peat is better for setting the pH of the mix, however, it is sometimes replaced with...
• Coir: coconut fiber is also great for drainage, and since it is a by-product, it's more accessible than peat.
• Bark: it increases the air space, and also improves drainage. Bark is a great choice if you plant to use the mix for a more mature plant that does not need constant wet conditions like seeds do.
• Vermiculite: vermiculite particles are like a sponge that can take up and hold nutrient and water and release them when the plant needs them.
• Perlite: this volcanic material helps balancing the drainage - air space - water retention of your mix. It is lighter and more expensive than sand, as has a couple of disadvantages, like floating on the top when the medium is watered.

A basic soilless mix may contain 4-5 parts of peat/Coir, 1 part vermiculite, 1 part perlite. Other mixes also exist, like not-really-soilless ones which contain compost, or enhanced mixes with added nutrients.

Is it better than soil? It is different. Of course, soilless mixes possess the following advantages:

• They are sterile: no soil-living pathogens, nematodes or bacteria will be there to harm your seed and seedling. On the other side, your plants may also miss the useful bacteria and fungi that are their natural, symbiotic companions. Lose one, gain one.
• It is easier control nutrient and water cycles: it is very hard - and in terms of time, slow - to set the right drainage, water-holding capacity and nutrient content for your soil. There many synergies, and even more antagonisms that should be solved or by-passed. With soilless media, you have to worry less about these problems.
• It is less compacted: no matter what you do, irrigated soils can become compacted quickly, and that can slow down or every prevent the germination of seed. The components of soilless mix make the medium more lightweight, so your plant can establish easier.