What is actually the downsampling of 2 mean?
If I have an image size of
256x256x170 and if I downsample it by a factor of 2, it will result in an image of size
Yes, that is correct.
Similarly, upsampling or resampling is the opposite interpolation method to original size
Yes, correct result again. Resampling is a more general term and describes resizing an image (or other grid-based signal) using an automatic rule which could be enlarging or reducing the size.
What resampling does not mean in digital signal processing is going back to the original source and taking a second sample. That might be a reasonable interpretation of the word when coming across it for the first time, but it is not correct here.
Just saying that a signal is resampled does not give enough information to say exactly what was done numerically to the signal, because it does not specify the rule of what happens with the lost (in case of downsampling) or missing (in case of upsampling) information. There are a few different ways to perform the resize, and different kinds of interpolation. It looks like the paper does give more information here, but you may need to read more or inspect the authors' code to be certain - for instance "nearest neighbour interpolation" probably involves looking at values of the six adjacent voxels to each new one you create, and taking the mean value of the ones that exist in the original grid (some will not, they will be other new cells), but there are a few different ways to manage that process.