Private IP means the router WAN IP is in the private IP range. This is because the ISP ran out of IPv4 addresses and therefore made several customers share the same public IP. Basically it's like a double NAT connection. You can't host anything with this type of connection because there is no public IP that can directly route to your router.

Public IP:
Internet----- (public IP) home router (private IP) ------ internal home network

Private IP:
Internet-------- (public IP) ISP router/NAT-------- (private IP) home router (private IP) ---------- internal home network