The volatility depends on both and strike.
It is specified by a object containing volatilities for various (maturity,strike) combinations.
The first dimension must span the maturities and the second the strikes.
Note this type only makes sense if the entry defined within Vol Spec supports the notion of "strike".
It is implemented either through the QuantLib CapFloorTermVolSurface or BlackVarianceSurface, depending on the referenced quantity.
In the BlackVarianceSurface case, a separately supplied user-defined two-dimensional interpolation scheme is also needed for those dates and tenors that do not appear in the Table2D
Otherwise linear interpolation and flat extrapolation is assumed.