While Lacy Razor got us started down the road, the art of soapmaking has so much more to offer. For starters, soapmakers refer to the "qualities" of a bar of soap. Stability and hardness contribute to a longlasting bar of soap. In some instances (such as shaving soap) a good lather is important. The moisturizing and conditioning qualities are discussed at a couple of levels. Many different ingredients contribute to these qualities (such as salt or goat milk), but one that can make a huge difference is the type of oil that you use.
Here's a quick list of the qualities and the types of oil that affect them.
Hardness, stability – palm, beef tallow, lard
Lather – coconut, castor, palm kernel
Moisturizing, conditioning – olive, canola, sunflower, soybean
Luxury, super moisturizing – cocoa butter, shea butter, almond, hemp, jojoba
Some oils provide more than one quality, for example, shea butter and coconut make hard bars of soap in addition to their moisturizing and lathering capabilities.
A check out this site to learn more about the qualities of soap making oils.