An obsolete Mac is a mac that can no longer receive service (A.K.A repairs) because ARSs (Apple Retail Stores) and AASPs (Apple Authorized Service Providers) generally no longer keep the parts in stock anymore.
According to Apple, an Apple product becomes obsolete 7 years after Apple stops selling them. Essentially, this means that the product in question cannot be repaired after that 7 years has passed, at least not by an ARS or AASP.
However, there are rare instances where some service providers, usually those that aren't considered authorized, may carry the parts and be able to fulfill repairs. It is incredibly difficult to find service providers that can fulfill repairs for an obsolete device and still carry the part, however, so don't count on being able to find someone who will still service your product.
For some Apple users, this can be really discouraging. However, remember that all devices have a threshold, and that carrying all the parts for all the many devices made would be incredibly challenging. Not to mention, once a device is out of date, and that technology is out of date, upgrading may be your best option in order to keep up with the accelerated advancement of technology.
Alternatively, having an obsolete Mac doesn't necessarily mean you need to upgrade. It just means that you will have difficulty repairing your Mac once it is obsolete.