A level-luffing crane is a crane mechanism where the hook remains at the same level while luffing: moving the jib up and down, so as to move the hook inwards and outwards relative to the base.
Usually the description is only applied to those with a luffing jib that have some additional mechanism applied to keep the hook level when luffing.
Level-luffing is most important when careful movement of a load near ground level is required, such as in construction or shipbuilding. This partially explains the popularity of fixed horizontal jibs in these fields.