The sample rate is the number of samples per second; eg. a CD contains 16 bit / 44.1 kHz PCM which means 44,100 16 bit samples (numbers) for every second of audio.
If you set the output of the card to a rate that is different than the source it will resample and in general there is no benefit to doing so for playback. Resampling involves interpolation, in other words 'intelligent guessing', to create more samples in between the original ones so that there are more. There can be a small benefit in that quantization noise is pushed into higher frequencies but it is very difficult to really hear any difference as you've noticed.
If you are passing DD or any other encoded digital format you do NOT want to resample as resampling will destroy the encoding and the AVR will no longer recognize it as DD.