"Novosibirsk" means nothing actually, because there was no "Sibirsk" city to make a "Novo-". "-sk" is an adjectival suffix. For example, river Irkut => "grad (city) Irkutskiy" => shorter form: Irkutsk. Then, "sibirsk" could mean "sibirskiy" (Siberian). Ok, enough.

According to some sources, "sibir" meant "sleeping land" in turkic languages. That's all I know.

The title of Novosibirsk was selected in 1925. It was Novo-Nikolayevsk (in honour of Nicolas II), and the progressive revolutionary state couldn't stand such a thing. There were tens of titles proposed, including Kaliningrad, oh, I don't remember now, but they were awful. "Novosibirsk" was accused right in meaning nothing, but fortunately it was selected. I'm happy that the neutral name was selected.