Foam covering around foundation--what is it and can it be removed?
Almost certainly XPS (Extruded PolyStyrene) foam insulation, R-5 per inch, inadequately protected. Colloquially known as blueboard though at least one brand is pink, and other colors are certainly possible.

You'd do better to repair or replace - uninsulated concrete is a superhighway for heat (whether cold out or hot out) and thus expensive to have showing.

Proper protection involves an adequate layer of a fibered stucco or similar product over the foam to protect it from sunlight and physical wear. Among other things visible in your picture is that the soil settled and the stucco did not extend low enough to account for that settling (or additional soil was not placed to compensate - either would have helped) as well as some severe physical abuse removing chunks.