Which networking mechanism translates private internal IP addresses into…

Correct answer: NAT (Network Address Translation).

NAT is the network-layer (Layer 3) mechanism that rewrites the IP-address information in packet headers, translating the private internal IP addresses used on a local network (the RFC 1918 ranges 10.0.0.0/8, 172.16.0.0/12 and 192.168.0.0/16) into one or more public, internet-routable IP addresses, and back again for the return traffic.

This lets many internal devices share a small number of public addresses, which conserves the limited IPv4 address space and is a major reason NAT became widespread. Because external hosts only ever see the public address of the NAT device, the internal addressing scheme stays hidden from the outside network, giving an additional measure of privacy/security.

So the single device described in the question - translating private to public IPs while concealing internal addressing - is NAT.