As the name suggests, domiciliary is something that happens at or is related to a person's home; so here, domiciliary hospitalisation is a situation wherein the patient receives medical attention at their home, it can involve hospitalisation at home for a grave illness/treatment which prevents the patient from moving and domiciliary hospitalisation is common in case of senior citizens. Domiciliary hospitalisation was at peak at when Covid-19 was spreading like a wildfire due to unavailability of hospital beds for patients. 

How to file for claim in case of a domicilary hospitalisation?

The procedure is identical to reimbursement claim procedure since cashless claim facility can't be used here. Just keep in mind that your policy covers domiciliary hospitalisation.