What the fields mean
An autonomous system (AS) is the network of one organisation: a provider, a host or a large company. The network shows the whole address block it holds, and the link opens it in the subnet calculator. Reverse DNS is the name the owner set in the PTR record, which often reveals the provider or what the server does.
How accurate it is
Country and network owner are reliable. The city is where the provider registers the network: for home broadband it usually matches the subscriber, for mobile networks and VPNs it may not. The radius next to the city shows the accuracy. For your own address, see What is my IP.