After hagbah, the one who lifted the Torah sits down with it and the someone else steps forward to do gelilah. This involves rolling the two ends of the Torah scroll together to meet in the middle, then dressing the Torah in its velvet robes and silver breastplate, bells and pointer.
Gelilah has a reputation as a second-class mitzvah, though this is thoroughly undeserved. It can require a high level of manual dexterity and co-ordination. The Shulchan Aruch writes that gelilah was more important than being called to the Torah and therefore the most distinguished member of the community would take that role.
The Mishnah Berurah, however, writing in the late 19th century, records that this was no longer the universal custom and that in some communities even children were given the honour of gelilah. Maybe their small fingers were an advantage. They were required, however to be able to understand that they were doing a mitzvah with a sacred object and not merely dressing an oversized doll.
The reason for the dressing the Torah in this way is that we should not hold it directly with our bare hands, out of respect for its holiness (Talmud Megillah 32a).