Overdischarging NiMHs is discharging an individual cell below 0.8V. Below that (when using multiple cells), the cell voltage can drop to 0 suddenly, and can actually reverse voltage (to something like -0.6V or so). Reversing the cell causes irreprarable damage, reducing battery life.
Fully discharging (also called deep discharging) cells also slightly reduces their life. There's really no reason to do a full discharge on a NiMH, except on occasion.
In fact, there's really no benefit to discharging a NiMH cell below 1.1V. There is only about a 5% difference in discharging a NiMH cell to 1.1V vs. discharging it to 0.8V.
(Note, the above is true for discharge rates of 0.5C or lower. At high discharge rates (1C, 2C, etc), that 1.1V threshold may be as low as 1.0V to 0.9V per cell, depending on how much the cell voltage drops due to the current being drawn from the cell.)
In fact, in packs or applications with a large number of cells (6+), it's better to call the pack "dead" at 1.1V/cell (so 6.6V for a 6 cell NiMH pack) to reduce the chance that a cell dies early and reverses voltage. For instance, a 10 cell pack has a voltage range of ~14V (fully charged) to 8V (assuming 0.8V/cell is dead), and 12V "nominal". Let's say you discharge the pack to 10V. It's entirely possible that you have 10 cells each at 1V/cell. However, it's also possible, due to one cell being weaker than the others, that you have 9 cells at 1.05V/cell, and one cell at 0.55V. Attempting to run this pack down to 8V will result in the reversal of the weak cell.
Even if you call the pack dead at 11V, it's possible you have 9 cells at 1.15V, and one cell completely dead (and near reversal) at 0.65V.
So, you can see the difficulty in preventing an overdischarged cell in large packs. That's one reason that battery pack makers in the RC racing world sell "matched" packs - packs where the capacity of the cells in the packs are closely matched (by doing several test charge/discharges of the cells to find their characteristics) so that all cells are discharged at the same time, allowing the pack to deliver the most power, and provide better performance.
