Re-usability of a used "pencil" (AA, or AAA) battery
Yes, you are missing something.
Depending on how you used it the battery might still have most of it's charge left or it might be almost depleted.

When a battery with a nominal voltage of 1.5 V measures 1.2 V and you just used the battery in a power hungry device (for example, a digital camera) then chances are that the battery still has a significant amount of charge left. If you leave the battery alone for an hour it will probably "recover" and measure 1.4 V or even 1.5 V.

In this case this battery might work again for a while in the high-power device. You could also use this battery in a low power device (for example: a clock or an LCD thermometer).

When a battery with a nominal voltage of 1.5 V measures 1.2 V and you didn't use the battery for a while or it is being used in a low-power device then "recovery" as mentioned above will not work. The battery has lost most of it's charge and is almost depleted. It is time to recycle it when the device stops working.

Edit: In case you want to learn more about this effect, watch EEVBlog Dave's video about the Batteriser where he debunks that product (on the grounds that there isn't much to gain from such a device) but while doing that he shows how the way you're discharging a battery determines how much charge you can extract.