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I can find the formation and info on Google, but can someone tell me what it really is? Its not in the Codex and from my understanding its got a different set of relics... Where can I find these?

Exterminatus in the Shields of Baal series. It does have different relics because it's a different Dynasty than the normal, but the Conclave itself is a Formation with a C'Tan Shard (which is house rules to be something else because it doesn't exist with that name) and two Crypteks. The Dynasty has a Detachment, a few other Formations and such, just like Flesh Tearers compared to Blood Angels.

Would you consider it to be similar to white dwarf formations?

...Sure? In the sense that they're both Formations that the army can use in any game, yeah. I don't think I really know what you're asking.

The Exterminatus book is two Blood Angel Supplements and this Necron one. Just like Sentinels of Terra, Haemonculus Covens, Black Legion or Champions of Fenris. Alternate ways to use the Faction and Formations that go with them. But nice thing about Formations is that they're self contained so it makes it simple to include Conclave of the Burning One into any standing Necron army.