An email Blacklist is a real-time database that uses criteria to determine if an IP is sending email it considers to be SPAM. There are several blacklists including SpamCop and Barracuda Reputation Block List. Each list will have it's unique way of accepting inbound mail and determining if email is considered SPAM. They can all impact deliverability for your emails. 

The diagram from Spamhaus below will help you understand the process for how a blacklist works. If inbound mail does not meet requirements to determine legitimate mail, then it is added to their blacklist. Some ISPs will use this data to influence their filtering decisions and delivery for email sent from that IP. The blacklist is a tool that helps ISPs make filtering decisions, they do not control the delivery or placement of your emails.

If you don't receive alerts from your email service, the best way to check if your IP is added to a Blacklist is to search the top Blacklist providers such as:

The key to understanding the ways to get off the Blacklist, will be understanding how you got on the Blacklist to begin with. Luckily, most of the DNSBL sites will provide instructions on how to be removed. The biggest culprit is usually spam complaints. Make sure you're sending to segmented and targeted lists and that you are proactive about improving your reputation by sending engaging content and campaigns.