You were expecting that to mean something filthy, weren't you. But, nope, not this one. The word comes from either the family name for the true thrushes, Turdinae, or directly from its source, Latin turdus, thrush, and is another in the series that includes feline (of or like a cat), canine (of or like a dog), lupine (of or like a wolf), and so on.
Despite its lovely voice, the nightingale is all in all quite turdine.
With an extensive gallery of photos, all in all it's a very turdine website.