Having a security question is a useful way to verify you own your account if you ever lose access to it.
You can add a security question to your account from your Security Settings page:
Click the account menu at the top right of any Facebook page and choose Account Settings.
From the left column menu, click Security.
Click on the Security Question section and follow the onsite steps. Note: You won't see this section if you've already added a security question to your account.
Tips for picking a good security question:
Pick a question and answer you know you'll remember
Keep your security question a secret
Make sure your answer is specific enough that it can't be guessed easily
You can improve the overall security of your account by updating your security information.