When typing an open interval as $]a,b[$, a closing bracket is being used in place of an opening fence and vice versa. This leads to the wrong spacing in, say, $]-a,b[$ or $A\in]a,b[=B$. The package attempts to solve this using:
\interval{a}{b} -> [a,b]
\interval[open]{a}{b} -> ]a,b[
\interval[open left]{a}{b} -> ]a,b]

The package also supports fence scaling and ensures that the enclosing fences will end up having the proper closing and opening types.

TeX maths does not do this job properly.

The author is Lars Madsen.