Model
A model is the trained program that turns an input into an output, learned from examples rather than hand-written rules.
What it tells you about a developer
Most developers who say they work with models are building software around a model someone else trained. Training a model and using one are different jobs with different skills, and the same phrase on a resume covers both.
A model is called that because it models, or represents, patterns found in its training data, the way a scale model represents a real object. Rather than a developer writing out every rule by hand, a model learns its rules from examples during training. A language model, an image model, and a voice model all follow the same basic idea applied to different kinds of data. When a developer says they are working with a model, they mean the trained program, separate from the rest of the application around it.