A blacklist in SEO is a list of spam users or websites that the major search engines or vigilante white-hat users compile. If your website is on a search engine blacklist it's highly likely that your site will be penalised or banned completely.
Websites that are caught by a search engines algorithm indulging in black hat tactics are likely to be blacklisted. Being blacklisted can be the death of a website so if you're outsourcing your SEO you should be very clear about the tactics they are using to rank your site.
There are thousands of databases that compile lists of abusive hosts and as the search engines crawl all these lists, being on any of them is potentially fatal. There are a number of tools you can use to search for your domain in these lists, one of the more popular being blacklistalert.org. While this tool can alert you to your site being blacklisted, it cannot help you remove your site from danger.
If your site is blacklisted by Google, you'll likely be listed by the other search engines too. You should follow the support instructions from Webmaster Tools to get your site back up and running and to make sure you get rid of any malware that may be lurking around. If you have been blacklisted by using black hat SEO techniques – stop what you're doing!
Sometimes, being blacklisted can be through no fault of your own and simply be the result of hacking. You should review your website's security frequently to ensure you reduce the chances of falling victim. Here's a fantastic step-by-step recovery guide to help you out if you find that you have been blacklisted due to hacking.