A Divisia index (or aggregate) is a measure of money supply that, rather than simply adding up the various components of money supply, attaches a weight to each component.
The justification for doing this is that not all money is held purely to make transactions with. Some types of money are clearly held primarily to use for transactions (e.g. physical cash, deposits in current accounts) while others are held primarily as a store of wealth (e.g. long term bonds).
A Divisia monetary aggregate assigns a weight to each type of money depending on the extent to which it is held for transactions.
Thus notes and coins would receive a high weighting (1 or very close to 1) whereas long term deposits would get a much lower weighting, and instant access savings accounts something in between.
The Bank of England Divisia index is based on components of M4. It uses interest rates to calculate weights: the higher the interest rate, the lower the weight.
The assumption is that interest rates are a good measure of why a particular type of money is held: the higher the interest rate, the more likely it is to be held because of an investment motive rather than to fund transactions. This appears to be a sound assumption as the main reason for accepting lower rates is to keep money more readily available for transactions.
While Divisia indices seem to be theoretically more correct than simple aggregates, they are a comparatively new development and have not yet as widely used.
Divisia indices are named after their originator, Francois Divisia.