A blacklist, as name implies, is a list of people or companies who have met with disapproval of others. In online world a blacklist refers to those people who have been marked as responsible for generating spam in a very big way. Blacklists are also known as blocklists.
Blacklists are used to combat spam in a very specific way. When spam is reported to one of relevant spam fighting organizations IP address spam originated from is added to a banned or blacklisted IP addresslist. An IP address is unique location of you or your website on Internet - think of it as your "home address" online. To put it simply every www.domain.com Internet address has a matching IP address. Any email coming from your website domain also has a corresponding IP address. If your IP address is present on a blacklist then you're potentially wasting your time sending email to customers.
Why are you wasting your time? Modern spam blockers come with most common blacklists installed and/or allow you to import updated blacklists into your spam blocker. This allows to you block a huge amount of spam but you may also, potentially, block legitimate email. Blacklists are not foolproof.
There are two types of IP address:
Dynamic - changes every time you connect to Internet. Most commonly used for dialup Internet access. Spammers love these because they're very hard to track and 100% disposable.
Fixed/Static - All websites, most large companies and some individuals use fixed IP addresses. This can cause huge problems if they're reported for pamming.