In my post, Dividends:  Common Structures, I talk about the three commonly used structures by which VCs accrue dividends.  The motivation behind each dividend structure varies. 

When Declared
The when declared structure is designed to ensure that the VCs aren't excluded from dividend payments.  This prevents the board from declaring dividends that only pay other share classes and leave the VCs out.

Cumulative
Cumulative dividends enable VCs to be compensated for investments that take longer to liquidate.  From an investor perspective this makes sense as the longer it takes to realize an investment (have the company exit) the worse their returns looks to the investors in the venture capital fund.  As a result, by accruing dividends a VC's return can be enhanced partially offsetting the effect of having a longer duration to liquidation.

Compounding
Compounding dividends can substantially increase investor returns over time.  While some VCs will use this structure simply to enhance returns, this approach may also be used to create incentive alignment.  In unique situations where there is either 1) additional risk to holding onto an investment for an extended period (e.g., a patent expiring) or 2) where the is concern that the entrepreneur will not be seeking an appropriately timed exit. 

In the situation of the patent expiration, the value of the exit may decline over time.  Having compounding dividends enables an investor to increase their liquidity preference thereby increasing the percentage of the exit value that they will have rights to as the company's value declines.  This may have the effect of stabilizing a return.  Conversely, in this scenario the operators will receive a smaller percentage of the payout as time passes creating an incentive from them to sell the company early.

In the second situation, where the investors are concerned about the entrepreneur's intent to pursue an exit, the compounding dividends does create an incentive for the entrepreneur to consider the timing of the sale (in addition to the size of the exit).

It's worth noting that it's most common to see the when declared or cumulative dividend structures in term sheets.