Properly, Head-driven Phrase Structure Grammar (HPSG). Developed by Carl Pollard and Ivan Sag (with some useful revisions by Bob Borsley), HPSG is one of several nonderivational theories of syntax, in contrast to the various incarnations of TransformationalGrammar. In simplified terms, HPSG is a type of PhraseStructureGrammar? in which syntactic structures are specified by properties in feature hierarchies that make up the lexical entries of words that act as heads of phrasal structures. For example, in Sally put the book on the table., the word put "knows" (i.e., its lexical entry requires) that it needs to be followed by a noun phrase (the book) and a prepositional phrase (on the table) to be a complete verb phrase. Its lexical entry further requires that it have some subject (Sally) preceding it in order to be a complete declarative sentence.
Obviously, things get a lot more complicated than this. For further discussion, see Head-Driven Phrase Structure Grammar by Carl Pollard and Ivan Sag, ISBN 0226674479
Contributors: SteveConley