What does metal-dependent mean?
It means that these enzymes need a metal ion as a co-factor for their function. This metal ion is typically bound somewhere near or in the active center and helps stabilizing transition states.

Without these metals, these enzymes cannot function properly, that's why chelating agents are used in protein or DNA preparations to inhibit their function.

References


Information available at cut rates: structure and mechanism of
ribonucleases.
The Role of Metals in Enzyme Activity