VPC NAT gateway

You can use Network Address Translation(NAT) gateways to allow instances from your private subnet to connect to the Internet and other AWS services, but not from the Internet to initiate connections with these instances.

It is “public subnet” that is set so that 0.0.0.0/0 (communication to the default gateway) flows to the internet gateway in Route tables is “private subnet”.

Since 0.0.0.0/0 flows to igw-xxxxxx (Internet gateway), subnet for which this route table is set is a public subnet.