What is a model in the context of IEC 61850?

A model is a model is a model ... huch.

The question is: What does a model provide? In short: It provides an external visible PATH to an actual value of something, e.g., a voltage or temperature. A model of my home is not something where I can life in! It shows where the rooms, stairs, ... are ... 

The leaves (or end points) of the model in the IEC 61850 TREE (of a model) are NOT where the actual value reside! Basic Data Attribute (BDA) in IEC 61850 are the leaves of the trees. 

Just a minor comment on the BDA: I found this: "This is the lowest level, where the actual value resides." IEC 61850 defines models that hide the storage location of an actual value. The BDA is a PATH to the actual value. The value resides "behind" that model. The BDA holds an externally non-visible or non-accessible reference to the actual measurement value or status.

When reading the current value of the phase A of the MODEL MMXU1 you send a read request with the PATH: "LD/MMXU1.A.phsA.cVal.mag.f". This PATH is translated into the direct or indirect storage location of a specific IED. How that is implemented, depends on the architecture of the interface and application software. It may even be mapped to an underlying fieldbus specific address (e.g., Modbus coil 2828). When the read request is received, the IED uses Modbus to read the actual value from coil 2828. In this case the actual value resides beyond the IED with its MODEL. The IED needs a non-visible specific mapping from the PATH to the Modbus register.

The models in IEC 61850 describe a virtual world in the following sense:

If it's there and you can see it         It's REAL
If it's there and you can't see it         It's TRANSPARENT
If it's not there and you can see it It's VIRTUAL
If it's not there and you can't see it It's GONE
Roy Wills

I hope that helps to understand the Models in IEC 61850.

This virtualization has an impact on how an IEC 61850 Stack (is not defined in IEC 61850 what a stack is) you purchase maps the leaves of the model to the location of your actual values.