The reason down-votes exists is similar to the reason up-votes exists. The total sum of votes should indicate how good an answer is perceived by the community. Good posts should be up-voted, not-good posts should not receive votes and really bad or incorrect posts should be down-voted.
You need to pay 1 rep for a down-vote on a question so that you won't down-vote just for fun and take it serious. If the post is deleted afterwards you can get your reputation back by recalculating it (go to https://tex.stackexchange.com/reputation#bottom and press the button there). If the post is improved by an edit you can remove the down-vote and get the reputation back as well.
Spam posts should be simply flagged as spam using the 'flag' link below it. You can down-vote it as well, but this is not required.