Hi-- not sure how close this is to the original, historical rationale for the use-it-or-lose-it policy, but my country's own recent experience shouldn't be very far from what you're looking for. So:

National budgets, as we know, are laws that are passed each year, allotting a certain amount of funds for specific projects. Before use-it-or-lose-it, less scrupulous departments would just drag their feet on the implementation of the projects-- the logic being that unspent funds would wind up as savings, which they could then allocate to projects of their own choice, without having to go through congress. Often, these savings would be reprogrammed into bonuses for officials and staff, or into pet projects where officials could get kickbacks. Use-it-or-lose-it stops this practice: Savings would end up back in the national treasury, basically narrowing the window for departments to reprogram their funds by themselves.

Consequently, it also incentivizes the quicker implementation of projects: If you don't use the funds for your project now, there's no guarantee that congress will pass the item in next year's budget deliberations. In fact, congress might actually cut your funds: "Last year we gave you x billion, and yet you were competent enough to spend only y of it in implementing your projects. This year maybe it's better if you only get x minus z, since you've shown that you're capable of implementing only as much, and so we can give more funds to other, more efficient departments." So departments, conceivably, would have to work faster and spend their funds faster, so that they can get more funds the following year.