Some subclasses of geometry (linestrings, multipoints, and multilinestrings) are either simple or non-simple. A subclass is simple if it obeys all the topological rules imposed on the subclass, and non-simple if it doesn't. A linestring is simple if it does not intersect its interior. A multipoint is simple if none of its elements occupy the same coordinate space. A multilinestring is simple if none of its element's interiors are intersected by its own interior.
The ST_IsSimple predicate function takes a geometry and returns 1 (TRUE) if the geometry is simple and 0 (FALSE) otherwise. For more information, see ST_IsSimple.