When you join a community as large as Stack Overflow, you're going to encounter people of all different kinds of professional and non-professional backgrounds, as well as every personality in between.
A fundamental truth about contributing to Stack Overflow is that in order to get upvotes, one must be prepared to face the fact that one will definitely receive occasional downvotes.
The best thing to do when you get downvoted is to let it go. Know that the rep lost from a few downvotes pales in comparison to the rep you gain from focusing on positive, constructive activities. A single upvote is 10 reputation whereas 3 downvotes is only -6 reputation. With 1 upvote, you're still ahead!
If you do get downvoted, a polite comment asking for feedback could get you a response that may help you fix whatever is wrong with your post. If you leave this comment, be polite. If yon can't be civil, then don't post a comment. The community may flag it and the moderators will delete it. Also, know that the feedback on your downvote could come from anyone, not just the downvoter, so again, be nice! In my experience, when asking for feedback, it generally comes from another passerby who agrees with the downvote and who kindly gives me information on what to do to fix the problem.
In some cases, I've even had the downvote removed, once I fixed the problem.
With that said, in this case, you may have done something to upset someone, or maybe your first downvoted answer prompted the user to look at some of your other posts. In general, it's discouraged to downvote people. Instead, content should always be the main focus of voting.
If this was serial downvoting, there is an automated script that may or may not kick in and reverse the votes. As Arjan pointed out, What is serial downvoting and how does it affect me? has more information on serial downvoting, as well as what you can possibly do about it.
Either way, my suggestion is to not get hung up on them. Doing so will only detract from the positive gains and contributions you could be making by asking other great questions or posting great answers. Hope this helps!