The term "battery memory" applies to rechargeable batteries
of the Nickel-Cadmium (Ni-Cd) variety. This type of rechargeable was the first major consumer
type, and is still used in many devices. It is a chemical
memory caused by recharging before the battery is completely drained
This is a common problem with cordless phones, as the cradle you hang the phone up on also charges the phone's battery whether it needs it or not. If you do not allow the battery to completely discharge before recharging, eventually you can only recharge it to the extent that it has been recharged most often. In other words, if the battery is capable of an hour's operation, and you recharge it often after only ten minutes of use, eventually the battery will only be good for ten minutes, no matter how long you charge it later
In the days before Nickel Metal Hydride (NiMH) and Lithium-ion (Li-ion) batteries, those who used rechargeables often, like those that used them in radio-controlled airplanes and cars, had chargers with built-in discharge circuits to prevent this very thing.