I've been hearing a lot about it but even having Googled the subject I'm not sure what it is or what it can do for me. I believe BDC's could be considered a BCS component? What is BCS?
Business Connectivity Services!
These are used when you want to pull data from other datasources/external data to SharePoint Environment, by other data source I mean it can be SQL Server database, Oracle, MySQL, Microsoft CRM, Microsoft Dynamics AX, in short anything!
What it can offer to you?
BCS can offer CRUD operations on your datasource using SharePoint forms.. Yes, you heard me! It can use existing SharePoint features like List Forms, InfoPath forms and work with your external datasource!
What are the options available to connect?
[Obviously you need to turn on BCS Services]
When you say WCF Service that means almost all of the external data sources are available which you can access through .Net Framework! Like as I said, you can connect to MySQL or Oracle.. There is no OOB option available but you can write WCF Service which connects to MySQL or Oracle and apply CRUD operations on them and utilize them as BCS connection! Also, there is an option to make your own CUSTOM BDC MODEL
Where to start?
Using SharePoint Designer you can start with making External Content Types, once External Content Type is set up you can generate External List from your External Content Type and the functionality added to External List depends on whatever operations you have defined in External Content Type!
Limitations on External Lists/BCS:
Other information is available on Internet, this was from my experience :)
You will get more idea when you will check the following url: http://msdn.microsoft.com/en-us/magazine/ee819133.aspx
You should really go for official doc you know, in short BCS enables you to communicate with external system data, but there are various aspect of BCS for which I think you should read some microsoft posts, you will find thousands of article online, here are some to get you started - Overview of Business Connectivity Services, Understanding Business Connectivity Services