Broadly, it's using an animal that is sufficiently like a human that it probably behaves similarly in whatever way is important for the study.
In practice they also often inbreed them to make them as identical as possible, and sometimes to induce specific changes. Ex: breeding mice that all get lung cancer would be an animal model of (human) lung cancer.
There are also transgenic models, where you might insert a human gene into a mouse to create a model of human disease, ex: inserting a huntingtin gene variant to induce Huntington's in mice and create a mouse model of Huntington's.
It's any animal (mice, in this case) with a set of characteristics you keep constant between trials. It could be mice of the same age or weight or that have a specific gene or have the same diet.
In practice they also often inbreed them to make them as identical as possible, and sometimes to induce specific changes. Ex: breeding mice that all get lung cancer would be an animal model of (human) lung cancer.
There are also transgenic models, where you might insert a human gene into a mouse to create a model of human disease, ex: inserting a huntingtin gene variant to induce Huntington's in mice and create a mouse model of Huntington's.