Developer Edition (often referred to as a "DE org") is a fully-featured development environment with limits on data and users.
An environment lets you instantly start developing, testing and deploying your software-as-a-service application, and you don't need to touch a single server, they're provisioned in the cloud. The Developer Edition comes with a number of applications pre-installed, including Salesforce CRM applications like Sales, Call Center, Marketing, and Ideas - in case you want to build extensions to these. There are many more types of environments (obviously not all of them are free!) - for example there are environments for testing and for unlimited production deployment. These are described in An Introduction to Environments.