A ductless or ventless range hood is simply a recirculating type of range hood. Instead of ducting or venting the exhaust air to the outside world, a ductless hood extracts the steam from your cooktop and passes it through some metal filters (to trap the cooking grease) and then recirculates the cooking air back into your room.
Most have no filters but some rangehood models do come with a charcoal filter installed. The purpose of this filter is to eliminate cooking smells and odours from recirculating back into your room. The filters are made with activated carbon (which is an extremely porous substance). Cooking odours simply get trapped inside the carbon particles. Charcoal filters typically have a short life span of approximately 3 months (depending on the frequency of use) and they must be discarded and replaced with new charcoal filters because they cannot be cleaned and re-used.
Ideally you should try to duct or vent your range externally. Some times it is just not possible to do this. For example, the rangehood is mounted to an internal wall, restrictions may be put in place by the body corporate (or strata managers), you live in a high-rise apartment etc. In these situations a ventless hood is most appropriate.