What exactly are Bitcoin Days are why are they destroyed? To answer that we first need to understand how Bitcoin works under the hood.

The entire Bitcoin supply is in fact a huge collection of coins collectively stored on the blockchain. Every coin (which technically is called a UTXO or unspent transaction output) can have any nominal value unlike with the regular money which have set denominations of 1, 2, 5, 10 etc.

When address A owning a coin of, say, 3BTC denomination wants to 'send' 1BTC to address B, she must spend (or destroy) the entire 3BTC coin and create 2 new coins- 1BTC with the ownership assigned to address B and 2BTC assigned back to address A. There's no way to partially spend a coin.

Now if address B holds 1BTC for N days until today, we say that the coin accumulated N Bitcoin Days. If this coin is now getting spent these become N Bitcoin Days Destroyed.

Interpretation. A big number of Bitcoin Days Destroyed in any given period indicates a large distribution of old coins by long term holders (smart money). All previous market peaks have been accompanied by a period of elevated destruction of old coins hence the metric can be used to catch the late stages of bull cycles.

To further account for ever-growing supply of Bitcoin and thus a potential to accumulate/distribute a bigger amount of Bitcoin over time, we can apply a supply adjustment multiplier to the metric.
`"TotalSupply" / "CurrentSupply" * sum_(i=1)^n "CoinAge"_i * "CoinValue"_i`
This multiplies effectively magnifies earlier days data when the current supply was still low. One can argue that instead of doing that we must be magnifying the more recent data which is more topical to the current conditions - price, Bitcoin narrative, adoption, macro condition etc.

To do that we can reverse flip the multiplier which produces the second variation of the metric called terminal adjusted BDD.
`"CurrentSupply" / "TotalSupply" * sum_(i=1)^n "CoinAge"_i * "CoinValue"_i`