Trace--Referring to the liquid soap at the thick stage, reached after mixing throughly. Signs of trace are thickened liquid that you can slide a spoon over and it leaves a little trace or dent.
Saponification--The chemical process in which lye and the oils and fats react and turn into soap. Broken down its basically a Base (lard/oil) reacting with an acid (sodium hydroxide or lye) to make a "salt" (soap).
Seize--Referring to when your soap does not turn out right due to a fragrance or color that your put into the batch during trace. Usually, it turns into a big sticky glob. Some people say that you can melt it back down, but I always just toss mine and start anew.
Cure-- The period which you set your soaps out to "dry" in order for them to reach maturity. They will lather better and last longer, but you can use your soap a day or two after you get them out of the mold. I have used mine as soon as I took them out because I was out of soap.
Green--Referring to how old a soap is, the greener it is, the younger it is.
Essential Oils (EO) --Natural fragrances that are derived and concentrated. They do not fade away easily, but they are MUCH more expensive.
Fragrance Oil (FO) --Man Made fragrances that are made through a chemical process. They have a tendency to fade away faster than EOs, but they're a lot more affordable if your little hobby isn't bringing in the bacon as you hoped. Just give it time.
Mold --The box that you sit your soap in to set. They come in a variety of shapes and are made out of a variety of materials from cardboard to wood. They now come in bendable plastic materials that are much easier to remove soap from than those made of hard plastics/wood. I still use a cardboard box lined with a plastic liner. It works better than all of them, in my opinion.
Color Chips--Solid coloring agents for soap, they are poured in at trace and melt in with your soap. They are made from food grade coloring suspended in stearic acid (the same thing that crayons are made out of. This is the reason that you can use crayons to color also, though many people, including myself don't like to do that.)They can also be used for candles, but never buy candle coloring cakes unless they say they're safe to use with soap.
Liquid Color--Just what it sounds like, liquid color. But, don't use your regular food coloring as it is water based and will just not turn out right. I've tried it, and messed up an entired batch of soap. Always make sure that the color you're using for soap is good to use.
Powdered Colors--Powdery coloring agents, usually made from rocks or clay. These work best as they are natural.