It says here that
The unbounded array is similar to a std::vector in that in can grow in size beyond any fixed bound. However unbounded_array is aimed at optimal performance. Therefore unbounded_array does not model a Sequence like std::vector does.
What does this mean?
As I understood it from the linked documentation, it is all about allocation strategy. std::vector afaik postpones allocation until necessary and than might allocate some reasonable chunk of meory, unbounded_array seams to allocate more memory early and therefore it might allocate less often. But this is only a gues from the statement in documentation, that it allocates more memory than might be needed and that the allocation is more expensive.
It appears to lack insert and erase methods. As these may be "slow," ie their performance depends on size() in the vector implementation, they were omitted to prevent the programmer from shooting himself in the foot.
insert and erase are required by the standard for a container to be called a Sequence, so unlike vector, unbounded_array is not a sequence.
No efficiency is gained by failing to be a sequence, per se.
However, it is more efficient in its memory allocation scheme, by avoiding a concept of vector::capacity and always having the allocated block exactly the size of the content. This makes the unbounded_array object smaller and makes the block on the heap exactly as big as it needs to be.
As a Boost developer myself, I can tell you that it's perfectly fine to question the statements in the documentation ;-)
From reading those docs, and from reading the source code (see storage.hpp) I can say that it's somewhat correct given some assumptions about the implementation of std::vector at the time that code was written. That code dates to 2000 initially, and perhaps as late as 2002. Which means at the time many STD implementations did not do a good job of optimizing destruction and construction of objects in containers. The claim about the non-resizing is easily refuted by using an initially large capacity vector. The claim about speed, I think, comes entirely from the fact that the unbounded_array has special code for eliding dtors & ctors when the stored objects have trivial implementations of them. Hence it can avoid calling them when it has to rearrange things, or when it's copying elements. Compared to really recent STD implementations it's not going to be faster, as new STD implementation tend to take advantage of things like move semantics to do even more optimizations.