A common alternative translation of the first two lines is "The Tao which can be spoken is not the eternal Tao/The Name which can be named is not the eternal Name."
Both translations make it clear that any discussing one does about the Tao will be necessarily incorrect. The general theory is, it seems to me, that the Tao is beyond capturing in language. We have no reason, however, to take this assertion on faith. Why is it that the Tao would be beyond language? Language is a powerful device with an infinity of expressive possibility. Our notion of infinity is that it extends-without-end, and thus it should encompass everything.
Mathematics, however, presents the notion of different MAGNITUDES of infinity. Language, being as it is built up of discrete entities (words) to form further discrete entities (sentences), in a process that can be compounded a discrete number of times, is capable of what is called a COUNTABLE infinity of arrangements. That is, using words the number of possible ideas conveyable is equivalent to the number of Natural numbers (1, 2, 3, etc), but LESS THAN the number of Real numbers (those numbers existing on a continuum, including the Natural numbers, fractions, and all decimals, including non-repeating, non-terminating numbers such as pi).
If we accept the notion of the Tao as flowing across all things, that very notion of "flowing" suggests a continuum. The Tao, then, would logically be unbindable by language, for it expands past the information set expressible by language.
The first stanza of the translation presented above conveys slightly different meaning, it seems. It begins by separating the Way--tied to experience--from the world--tied to construction. There is here a separation between the motion of the universe and that which performs this motion, a separation between nouns and verbs. In both sides of this separation, though, there is this declaration of impossibility. I would say that the impossibility suggested does not stem from the inherent impossibility of experiencing the Way or constructing the world, but rather from the semantic fact that the verb forms "can be experienced" and "can be constructed" imply a subject doing the experiencing and constructing. Later in the text, the understanding of the falseness of the ego becomes clear, but this is the first hint thereof.
It is clear that it is impossible to experience something unless one is separate from that something, at the very least in scale. The Way, then, is inexperienceable because we are, inherently, the same as the Way, without separation or border. The world is unconstructable because the constructing agents is the world, simultaneously and without separation.
The conclusion of that first stanza reaffirms this notion. The Way is everything manifest, the world is everything represented. It should be noted that even that which is impossible is contained by the Way and the world, because even the impossible "may happen" and "may exist," if only the rules governing the possible change (rendering the notion of "impossible" obsolete).
The next stanza is one of my favorites. We see here a beautiful separation that resolves itself into a state wherein dichotomized entities are resolved into a single identity. Experience with and experience without abstraction are understood as identical endeavours. When we experience without abstraction, we have direct access to the phenomena which we experience, which gives us total understanding of those phenomena. When we experience with abstraction, we have a theoretical understanding of the motion and mechanisms of the phenomena in question, in which case we can still (theoretically) achieve total understanding of the phenomena.
This stanza also hints at themes of unity present throughout the text. What appear, initially, to be entirely separate ways of experiencing the world are, indeed, the same. They are simply different ways of approaching the same end.
The final couplet is an enigmatic piece of poetry. What I get from this is an expression of the over-arching presence of the Way. To say what the Way is would be inherently incorrect, as discussed earlier, but we do know that it is "greater and more subtle than the world." The world, understood as those constructed objects which are the positive-space Yang of our reality, stand on top of and against the Yin that is space. I think it is fair to assume, given the later themes of harmony, that Laozi would not have understood the Yin to be "greater" than the Yang (although perhaps, admittedly, more subtle), and as such we realize that the Way is something greater than the might of the Yin and the mystery of the Yang.