When a person is questing, that means that they have an item that they really want, or a certain look that they want to achieve, and they "quest" to earn gold to get that item or that dream avatar.
Questing means that they save up gold. A person may also spend extra time on Gaia solely in the pursuit of earning more gold (like playing more Jigsaw than they normally would, or spending time on the Marketplace looking for deals).
You can find the SHFT Questing Guide here (it's in the Quest/Beg/Charities subforum of the guild). ^.^