In British English (and possibly others), backward and forward are adjectives, and backwards/forwards are adverbs.
A person may be backward1 or forward; a car may be forward of a "Stop" line; one might move something forward (that is, to a position which is forward of its current position). However, when describing that movement itself, it's forwards.
Related question: Meaning of "backwards"
1 Using backward to describe some developmental abnormality is frowned upon and not recommended. In fact, describing someone as forward is rather dated, too.