Do you move toward something or towards something? It turns out, you can do both, though some contexts favor one over the other.
According to the Chicago Manual of Style, the preferred form in American English is toward without the -s, while the preferred British English form is towards with the -s. This general rule works with other directional words, including forward, backward, upward, and downward, along with afterward.
However, what applies to formal written English does not always apply to informal settings, both written and spoken. American English speakers often use towards in colloquial speech and writing, and toward sometimes pops up in British English.
Additionally, things have not always been this way historically. For example, Chaucer wrote The Canterbury Tales in a time before English spelling was standardized. Despite being a British text, he uses toward without an -s, the accepted American English variant today. Looking at American English data from Google Books Ngram Viewer, towards appears to have been used more widely in American English texts up until about 1900, when it was overtaken by toward.
Which variant do you tend to use and why?