Definition of a model in machine learning
I was interested in the same question recently and came to the realization that there is no single definition of a "model" in machine learning. It's highly dependent on the sources you're consulting, which may be the documentation for a particular software program, the slang adopted by its user community, or the definitions used in published academic papers, which can vary widely from journal to journal. Moreover, I had to learn to keep in mind that such papers are written not just by specialists in machine learning, but by experts in other disciplines who have a need for applying machine learning techniques (such as imaging, various medical fields, etc.). Many of them do not explicitly define the term "model," which is often used loosely. Here are just a couple of different definition of "model" I've seen in all this widely scattered literature:

• Statistical models, particularly the stats related to probability distributions.

• Regression data and related statistics.

• Mathematical models as mentioned by Neil Slater above.

• The data models used in machine learning, such as the columns involved, their data types, the data sources and other metadata. This is particularly tricky because there's nothing mathematical about this definition at all, unlike the first three I listed. For an example, see all the documentation for SQL Server "mining models," which serve double-duty for machine learning purposes.

• Sometimes all of the definitions above are expanded to include machine learning structures built on top of the equations and the metadata, such as the specifications of neural nets. In other cases, these are considered separate entities. 

All of the above are sometimes mixed and matched together, depending on the source. I'm sure there are other definitions of "model" I've left off this list, which will complicate the matter even further. To deal with this ambiguity, I'm trying to train myself to divine the intentions of the author whenever they use the term "model." Sometimes it's easy to determine based on the context or the field the author works in, but other times I have to read deeply into an article or documentation before figuring it out. I wish I could be more definitive about it, but it's really a naturally fuzzy term; there's never going to be a simple one-size-fits-all answer to this. I hope that helps.