At the simplest level, a model is a system that takes an input and produces an output. That output might be a predicted class, a number, a score, a ranking, or the next token in a piece of generated text. The exact form changes from task to task, but the basic structure stays the same: input goes in, output comes out.
What makes it a machine-learning model rather than a normal hand-written program is how the behavior was created. In a traditional rules-based program, a human writes the logic directly. In a learned model, the behavior comes from adjusting internal parameters so the outputs line up better with example data.
That means the model is best understood as a learned input-to-output mapping. It is not helpful to start with dramatic language like "digital brain" or "machine intuition." Those phrases make the system sound mystical, when what you really need is a clear mental picture of what it is doing operationally.
If someone asks you what a model is, a strong beginner answer is: it is a parameterized system trained on examples so it can make predictions on new inputs. That answer is not flashy, but it is much more useful than hype.