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If all of the board elections occur on the same date, a majority of the board can be elected (by someone wanting to take control of the company) in a single election. With staggered elections, it could take several elections – hence, several years – to take control of the company.
Since majority of the board is not up for re-election every cycle, you cannot replace them and seize control. You have to wait for more elections to gain control during which time, the incumbents may take actions that are not in your best interest.
It’s pretty damn effective. Bebchuck (at Harvard) has studied this extensively. IIRC, pretty much no firm in his sample with a staggered board had a hostile takeover take place in something like 6 years.