When is it most adventageous to connect battery cells in series?

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A battery cell uses chemical oxidation-reduction reactions to generate an electric potential difference.  The amount of potential differences created depends on the specific chemicals in the cell.  A typical carbon-zinc dry cell battery will generate a potential difference of about 1.5 V due to the difference in electronegativity between zinc and carbon.

If a circuit that is to be run by batteries requires a voltage that is greater than that which can be created by a single cell, it will be necessary to attach more than one cell.  If the cells are connected in parallel (and assuming they have the same potential difference), the cells may last longer, but will not produce higher voltage difference.  If the cells are hooked in series, that is the positive poll of the first is connected to the negative poll of the second, etc..., the potential difference will be increased.  So, two 1.5 volt cells connected in series will produce 3.0 volts of potential difference.

Whenever it is necessary to produce more voltage than can be supplied by a single cell, connecting multiple cells together in series will increase the available voltage.

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