Why does "exercising" a battery extend its life?

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I have been told that if you have a rechargeable battery, such as in a laptop computer, that you should use the battery, running it down to a low level, in order keep it working properly, i.e., they keep their life longer. Do any of you know what is the reason for this?

For Li cells it is more for the internal charging circuit to calibrate its capacity and to try and equalise the cells to prevent one cell acting as a load and dragging down the efficiency of the combined battery pack, however with modern devices I think its more of a legacy piece of advice.

Generally though, its only lead/acid batteries that require equalising, as cell balancing can prevent sulphation and dangerous gassing, but this is by 'stressing' rather than 'exercising' the battery

I know some basic chemistry, but I don't know some of this terminology. What is "cell balancing"?

Take a 12v battery ( lead/acid) it will contain 6 separate cells producing circa 2v each. Due to small differences in surface area, and the temperature/acid mixture local to each cell, there will be differences in V and A produced by each cell. This can cause lead sulphate to be deposited on the cell plates that are not charged properly causing further deterioration of the effected cell. This can lead to more power being needed to charge with hydrogen being produced.
By stressing or overcharging you make the plates gas a little but it helps prevents sulphation.

As the voltage per cell between 0 and 100pc charged is fixed, a cell that is not working properly will loose amps quicker, and cause the voltage to drop in that cell, and creating a load to be supplied by the other cells operating at a higher A capacity.