Broadband Network Gateway. It is the equipment which terminates your connection which is coming via DSL or FTTH when the network between you and the BNG is Layer1 or Layer2 or the service is provided through PPPoE. This is mostly the case in India
In various countries, they use DHCP based service (IPoE) which can be provided by a Layer3 network also.
BNG is the device which authenticates you and apply right policy which enables 100Mbps. 200Mpbs etc on your line dynamically and also gives you IP address. This is done with the help of a software called AAA using radius protocol or in some cases it uses PCRF using Diameter.
Some OEM also supports integrated CGNAT in the same device and some do not and in their case the CGNAT will be a separate equipment between the BNG and the internet.
The latency problem is not addresses by the equipment. The latency is addressed by keeping the server as close to the BNG. In some cases the Ookla servers are directly connected to it.
If you notice in the Patna related thread, the latency is higher because there is no Airtel BNG physically present in Patna and the service is being provided either from Lucknow or Kolkata based BNGs. Even if they check it to the Ookla server hosted at Bharti Airtel Patna, they will get very high latency, but to lucknow it will be less that 10ms
Edit::
@shashankb Thanks for posting the URL