Forward is an adjective which refers to a movement to the front, it is also used in expectation of something.
"He moved forward or I am looking forward to the party."
When used as an adverb, 'forward' may be used with an 's'. 'Forwards' is mostly by Americans for its counterpart 'forward'.
"He ran forwards to receive his award."
Foreword is an introduction, usually to a book.
"I made sure the priest wrote the foreword to my last book."