In Michigan and in the context of landlord/tenant law, a writ of restitution is an order evicting the tenant from the property. It's essentially an archaic term for "order of eviction".
If you have been served with one of these, it is likely that you have been sued for eviction. Because you're entitled to notice and an opportunity to respond when being sued for eviction, you may want to contact an attorney if you haven't already done so.
This is provided as general information. No attorney-client relationship has been established. This information may not be appropriate for the facts of your particular situation. You should consult with an attorney before taking (or failing to take) any action based on this information.