"20/24-bit DAC" refers to the internal resolution that the DAC's reconstruction filter works at. This is independent (and unrelated to) the resolution of the bits coming in. More bits to work with internally usually means a more accurate filter, producing a smoother, less harsh and "digital-sounding" end result.
The 20/24 bit DACs perform interpolation of the 16 bit data. In very rough terms, it's equivalent to a let's say a 1200 dpi scanner, which uses interpolation software to produce a 9600 dpi image. The software uses the built in algorithms to add bit data that it deems logical. For example, if it sees data 1 3 4 6 8 9 10, it may add 2 and 5 in the appropriate places. That doesn't mean that 2 and 5 belong there, but it makes an assumption that they do.
So, to make a long story short, the 24 bit dacs fill in bits in the 16 bit data stream. The resulting output is a 24 bit interpolated data stream. Hope that made sense.