Constant item purchasing power accounting is a way of measuring someone's buying power, or the amount of stuff they can buy. To do this, we look at what prices they pay for items they need over a period of time, and make sure that those prices don't change too much.
For example, say Mary wants to buy a gallon of milk every month. We might look at the prices for milk over a year and see that it usually costs $4. However, if one month the price goes up to $5, Mary's buying power has decreased, because she now has to spend more money for the same gallon of milk.
Constant item purchasing power accounting takes this into account and measures how much Mary can still buy in other areas, such as apples or bread, to make sure her buying power stays the same. That way, if prices go up or down, Mary can still buy the same amount of stuff.