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Remember mathematics and the advantages of the logarithm: Multiplication is translated to simple addition.
Now think of a communication chain with various systems contributing to the overall attenuation (for example a satellite link).
The calculation of the overall attenuation including influences of system changes is simplified if you have an overall sum instead of a product.
---------- Post added at 10:46 ---------- Previous post was at 10:41 ----------
The answers from sherazi and klystron give you some additional advantages. For example, the well known BODE diagram can display in one graph very large and very low attenuation or gain values only if the logarithm function is applied.
AS LvW said plus, the original unit was the "Bel", this was used by telephone engineers for working out the losses on long circuits. When electronics came along and decent meters, The Bel was found to be too coarse, hence the Decibel.
Frank
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