As discussed here, a DNS leak is where DNS lookups ignore your current routing (in the example of a VPN connection) and still end up going out over your normal internet connection.
This can obviously lead to the anonymity provided by the VPN (in this example) being undermined and thus tools like DNS Leak Test and IP Leak still report your approximate location in addition to which ISP you use, etc.
How can I protect myself against DNS leaks?