Basically there are two different types of prints
1. Rubber (or oil based) print
this adds a colored paste in the shape of your print on top of the fabric. So practically this material covers the fabrics and therefore can be felt. It has a 'rubberish' hand feel to it (that's why it's called rubber print sometimes)
2. Water-based print
this is a bit more complicated. In order to achieve a soft hand feel (without the 'rubberish' touch) you can bleach away part of the original fabric color and then apply water-based ink to the bleached-away parts of the fabric in a second step.
The ink sinks into the fabrics and practically dyes it, therefore you achieve the the same (soft) handfeel as just the fabric by itself.
This method has some restrictions though. At first the costs are pretty high due to the bleaching paste being expensive plus a more complex procedure being necessary to actually come to the actual print. And furthermore it can only be applied to 100% Cotton fabrics. So all blends (Polyester, Spandex, ...) do not qualify