Syntax is the linguistic study of how words combine to form sentences. (To linguists, "syntax" is a subset of "grammar", and grammar also includes things like the study of valid word forms.)
There are many broad theories of how syntax arises, rooted in philosophical questions. Why are humans so good at language? How do humans acquire language so quickly, and why do they make some kinds of mistakes but not others?
One such theory is generativism. It posits that the human brain has an innate faculty for grammar, which places certain restrictions on the parameters of human languages. We can imagine a universal grammar "generated" by this innate faculty. There have been decades of efforts to describe this universal grammar, and show that human languages all over the world adhere to it in some sense. For example, human languages tend to have noun phrases and verb phrases.
This theory is not without criticism: there's little neurological evidence for an innate "language device". However, generativism has also been very successful in explaining natural language syntax and semantics at many levels. If we can describe Toaq's syntax in these same terms, we can be certain that it is a human language, rather than merely a way to "speak out loud" an unnatural mathematical or logical structure.
Hoemaı's attempts to describe Lojban syntax in the framework of generativism were unsuccessful, whereas efforts to describe Toaq with the same linguistic tools are working out (and Toaq is evolving with this goal in mind). This current description of Toaq syntax is influenced by X-bar theory and the Minimalist program. Toaq being a loglang means that we can unambiguously parse sentences into syntax trees. Zugaı is a piece of software that performs this transformation.