Tertiary means "third." You can configure multiple DNS servers, depending on the platform. Typically you'll have a primary and secondary (that's the case with my ATT ADSL account), but you can configure as many as your client (in this case the PS3) will allow. Or as many as your DHCP server will allow.
Check your client (the PS3) and your DHCP server. Though the answer may not be on target, but it's best to eliminate it first, as it's pretty simple.
Find out what it is by opening the command prompt on your computer (Start -> Run, type cmd, hit Enter) and entering ipconfig /all. This will list all the potential suspects. Keep in mind, though, that the DNS servers are probably a pass-through from whatever is acting as your DHCP server (probably your residential gateway/router). Depending on who made the router (Linksys, D-Link, Netgear, Belkin, etc.), you may have to do different things to see the DNS server addresses. You may also be able to see it in the graphical interface on your PS3. I can on my Samsung Blu-Ray player.
You may have to hard-code the DNS server addresses into your DHCP server. You probably aren't running a local DNS server, so are stuck with the values shown by your ISP. If the PS3 has room for three DNS servers, one of them is probably being left blank. Hence the solution of inserting the primary or secondary server into the tertiary server field.
Check your documentation for the PS3 and for your gateway or other DHCP server, and choose the easiest and least disruptive path. ISPs do change the addressing scheme once in a while, so if you can hard code this on your PS3 and leave the DHCP server alone, it will be best. If your PS3 stops resolving names in the future, you can still use your PC to get the current values with the ipconfig /all mentioned above.
Primary, secondary, tertiary, quaternary, quinary, senary, septenary, etc. From Latin. But this is getting way too geeky.