Document Center - This is meant for more of a document storage location, think about storing documents here similar to how you would a network share. This is a centralized location for information. It will always depend on your business needs as to how you would use this. The document centers in 2010 come with Document ID's enabled and a user interface tailored to quickly uploading documents.
Document Workspace is a place where you could work on a document or sets of documents with a team. Think of it as a place to work on an RFP for example. You can create a document workspace directly from a document that may reside in the Document Center. You could upload your research docs for an RFP to the workspace and edit your document in the workspace. The document would get updated in the Document Center.
Records Center - This is meant for storing records long term and making the records immutable so that they cant be changed or overwritten. This will come into play with items such as contracts, employee information. You can have workflow pass information to the records center and then use workflow to declare items records and start dispositions on the files so that in 7 years or whatever your timeline the document is removed from the environment.
There are many aspects to how you could use each of these. It is certainly going to depend on the business needs. If needing a records center you really should do a lot of planning up-front. If compliance is a big thing in your organization and you want to use SharePoint as a records repository you can make it DOD 5015 compliant with add on software from companies like Gimmalsoft.