TS3 has a global blacklist server that all clients connect to as part of the connection process for any TS3 server. If the client cannot reach the blacklist server, the client is not allowed to proceed with the TS3 server connection.
If you see this error, check to make sure that you don't have a firewall that might be blocking the connection to the TS3 blacklist server (which uses UDP). Also double-check that your DNS resolver is working properly; if you're not sure, try changing it to Google's, at 188.8.131.52. You can also try rebooting your router and modem.
If all measures fail, it could be that there is a routing problem between you and the blacklist servers. You may need to wait a bit and try again.