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Why the letter ‘A’ is written after the word ‘decibel’?
A-weighting: This is a filter which when applied to a measuring metre, converts its behaviour almost exactly as would a human ear. For many practical purposes, when simple direct readings are needed, this is the best scale to use. Since human ear response frequency dependent, the readings of the sound pressure on a linear scale can be misleading.

How do decibels add?
Decibel values cannot be added arithmetically; if there are two machines each making 80 dB SPL, the resultant noise is NOT 160 dB but just 86 dB !! This is a logarithmic addition.
 

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