Bitcoin days destroyed is a measure of volume in the Bitcoin network (and works equally well for other decentralised currencies) and quite a good one at that. It's the solution to the problem of how bitcoins can be quickly moved between addresses and create the illusion of volume when the bitcoins stay with the same person or company all along.
The thing that is being measured is the amount of time that the Bitcoins in a transaction have been at one address prior to that transaction.
For example, if 10BTC was at one address for 30 days and a transaction took place to move that 10BTC to another address then that transaction would have 300 bitcoin days destroyed. If the new owner of those 10 BTC then took them and immediately split them across ten different wallets then 0 days would have been destroyed (but volume statistics would register a further 100 BTC volume).
It's very useful for looking at blocks of transactions (which represent 10 minutes worth of all transactions on the network) because it allows you to sort out what blocks represent users moving the same bitcoins around a lot and what represents large transactions of bitcoins across the network and can be used to find hoarders offloading.
We looked at the data for 300 blocks and plotted volume against days destroyed. As you would expect they have a positive relationship but what's really interesting is the power law hidden in there.
So what does this tell us?
Firstly, since days destroyed is a function of volume (volume in a transaction times amount of days the bitcoins have been still) we can conclude that days static of bitcoin is spread evenly across large transactions and small transaction. Whether a transaction is big or small seems to have no bearing on whether the bitcoins have been static for many days or not.
We can also conclude that there's no natural upper limit to the number of days destroyed in a block but that as volume increases then the likelihood of many days destroyed does too.
It's also clear that much of the moving of previously static bitcoins around the network is happening in a low proportion of the volume - which should leave us distrustful of any volume statistic.
The next thing to investigate is whether the power function for their relationship has moved over time. This would give an insight into whether there's a shift in the network from person-to-person transactions to rapid transactions inside individuals wallets (something not conducive to economic growth).