Memory effect occurs when a sintered-plate nickel-cadmium (NiCd) battery is repeatedly discharged to a particular level above a full discharge, that is, only "partially used", and then re-charged to an equally precise "full" level. This "real" memory effect is extremely rare and is found only on very expensive, rare and older unattended electronics like communications satellites. Repeated attempts to duplicate it in the lab have proven difficult.
Voltage depression is a much more common effect that many ascribe to memory effect. In this case the peak voltage of the battery drops more quickly than normal as it is used, even though the total power remains almost the same. In modern electronics equipment that monitor the voltage to indicate battery charge, the battery is seen as being drained very quickly and therefore about to run out of power. To the user it appears that the battery is not holding a full charge, which seems similar to memory effect. This problem is a common complaint with high-load devices like digital cameras.
Voltage depression is caused by the repeated over-charging of the battery, which leads to the formation of small crystals of electrolyte forming on the plates. These can clog up the plates, increasing resistance, and thereby dropping the voltage of some of individual cells of the battery. This results in a seeming rapid discharge as those individual cells discharge quickly and the voltage of the battery as a whole suddenly drops. This effect is very common as consumer trickle chargers typically overcharge every time.
Urban legends about the memory effect, universally referring to voltage depression, have led to all sorts of quasi-religious behaviour in order to "fix" dead batteries. The most common suggestion is to completely drain the batteries in some other device in order to dissolve the crystals. While this works in theory, it more often leads to damage to the other cells in the battery, correcting the problem for a short time but leading to a considerably shorter overall lifetime.