I am looking at some data that is Delta 10, Delta 30, etc for an index option CDX IG. I know the meaning of Delta, as a sensitivity of the price move with respect $1 move in the underlying index. What does 10%, 30% mean in this case? Is that some subcase of the Delta I know?
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That is identical to how FX IVOL is quoted. See for example this question or look at an illustration showing how FX options are quoted in delta. Uwe Wystup and Dimitri Reswich explains this nicely.
I am not too familiar with CDS options, but if you have Bloomberg, you can look at CDSO. Each delta corresponds to a specific strike / moneyness. The vol surface can be found on OMON for CDX's. CDX IG 5Y Corp >> OMON - Vol surface for example. If you display it in moneyness, or delta is usually a bit dependent on markets and conventions. In your case it seem you have IVOL quotes in terms of delta.