Definition: When making soap from scratch, you must blend the lye-water and your heated oils until the soap reaches "trace." In days of hand stirring (which took hours!), trace was a sign that the soap was finally ready. Some people describe the "trace" as a little line, ridge or mound of soap that after you've stirred the soap and drizzled it back into the pot, takes a second or two to disappear back into the mix.
To test for trace, dip a spatula or spoon into the mix and dribble a bit of it back into the pot. If it leaves a little "trace" behind, you're there. The soap does not have to be really thick just yet, it just needs to be well mixed with no streaks of remaining oil.
Trace is a sort of "point of no return" in the soap making process. Technically, "trace" is when your soap has reached "emulsification" - when the oils and water have mixed and are not going to separate. Once your soap "traces", the mixture will not separate back into the original oils and lye-water. The soap does not have to be really thick just yet, it just needs to be well mixed with no streaks of remaining oil.That's the key thing to know.
In the photo illustration, notice the small ridge of soap across the middle. This was the dribble off of the stirring spatula as the color was being added to this batch (the purple on the left). This is what trace looks like.
Some soap makers prefer to pour their soap into the mold at "light trace", that is, immediately after trace is reached and the soap is still very liquid. Others prefer a more "heavy trace," that is, pouring the soap after trace has occurred, and the soap has thickened considerably. The trace on the right is a moderate trace.