The MailChimp API (application-programming interface) is a way for you to "sync" your customer database, CRM, CMS, or e-commerce shopping cart with MailChimp. It's really powerful stuff. MailChimp's API Documentation
An API is a software to software interface, rather than a user interface. Applications can talk to each other behind the scenes and work together without you ever having to see the programs talking to each other. For instance, when you import your list from Google Docs, MailChimp and Google are talking to each other behind the scenes, but you only see that your list gets imported. Your programmers can do the same thing for you, creating connections between your CRM and your MailChimp lists, campaigns and reports.