Consider a pot. We say that the pot is made of clay, but specifically speaking, the pot and the clay are not two different things. The pot is simply a form of clay. It is just clay shaped like a pot. If it weighs a few grams, how much of that weight is due to the clay, and how much is due to the pot? The pot adds nothing; . "vessel" is simply a name and a form; it is not an independent thing like clay. Clay can exist without the pot, but the pot cannot exist without the clay. What exists independently, like clay, is said to be "satyam", real; and something like the vessel, which has no independent existence, is said to be "mithya."
The same is true in the case of a gold chain. Gold can exist without the chain, but the chain cannot exist without the gold. So we say that gold is satyam, real, and the chain is mithya; its existence depends on gold.
Uddalaka used clay and gold as metaphors to represent the Brahman. By knowing the clay, all the vessels are known; by knowing the gold, all the jewels are known; and by knowing Brahman, the non-dual substratum of all that exists, the entire universe becomes known. Brahman is satyam and the world is mithya, because his existence is totally dependent on his underlying reality, Brahman.
To help his son understand this, Uddalaka explained, "vac-arambhanam vikarah namadheyam."
Vikarah: any shape or figure, like a vessel or chain, is "vac-arambhanam," based merely on words, ideas, or concepts. Similarly, "namadheyam", any name, like the name "vessel", is also based merely on words or ideas. Therefore "ityeva" (alone), "mrittika", (clay), is "satyam", (it is real).
The names and forms, which we refer to as "nama-rupa", are not tangible things. They are ideas or concepts rooted in thoughts and words, not in physical reality.
To say that the vessel is simply nama-rupa means that it has no physical existence unless it is associated with a substance such as clay.
When this metaphor extends to everyone, its implication is staggering. Everything we experience is merely name and form, nama-rupa. The world is only an appearance or form of the underlying thread of existence, the non-dual Brahman.