What is the proper procedure after saying the Brocho בורא מאורי האש? I understand you "look," but at what?
Based on the Shulchan Aruch 298:3-4 and the Mishna Berura there, the main "staring" is to ascertain that you have benefited from the light. The Shiur for this is the light enabling one to distinguish between 2 similar coins from separate countries. Since seeing the difference between light nails and darker skin is a similar shiur of light, and there is kabbalistic significance to looking at the nails (and palms), we stare at our nails to ascertain benefiting from the light.
The minhag al pi kabbalah is to fold your fingers down with your thumb on the inside and stare at the distinction, the fingernails and the palms. Then you open your fingers, folding the fingernails toward you with your thumb still folded in.
Fingernails are a bracha of growth, palm folds are also a bracha. The switching either has to do with a machlokes of how to interpret the zohar (magen avraham) or showing darkness to light for the front of the fingers (I forgot where I saw that. I can look around if anyone is interested). This is a short list. There are other reasons.