What is the physical significance of a complete boolean function
I have never heard of the expression "functionally complete" before so I looked it up.


  From the point of view of digital electronics, functional completeness means that every possible logic gate can be realized as a network of gates of the types prescribed by the set. In particular, all logic gates can be assembled from either only binary NAND gates, or only binary NOR gates. Source: Wikipedia, Functional completeness.


As an example, every logic gate can be assembled using the set {OR, AND, NOT}. We can do better than this though. Just using the set {NAND} we can create all the others:



Figure 1. Using only NAND gates we can construct NOT, AND and OR. NAND and NOR can be created by adding a NOT. NOR, XOR, XNOR and others can also be created.

In this sense the set {NAND} is functionally complete. The set {NOR} is similarly functionally complete. As a result these were most common gates used in discrete logic and also had the advantage of very short propagation time.

See Wikipedia's NAND logic and NOR logic for more info.