Why actually?
Anyone who has ever looked closely will have noticed that air plants also seem to have roots. One sometimes wonders why, since they absorb all of their water and nutrients through their leaves. In nature, these roots are the tillandsia's holding apparatus, anchoring them to their perch so that they are not carried away in strong winds or rain. When keeping and caring for air plants at home, these roots can be removed for cosmetic reasons. It is really important to only prune the brown, dry roots below the base. When pruning too high there is a risk that the plant will be harmed and run.
formation of new roots
When you see new roots developing on your tillandsia, that's a good sign as it shows that the plant is doing well and wants to make sure it stays in place.