By exercising early, you effectively own stock at the date of exercise. If the company goes public or gets acquired, your gains are already long term capital gains as long as it's been a year. Also, you don't have to wait once the company goes public to exercise your options, then wait a year... you can sell right away, lock-up periods aside.
To summarize, early exercise is a cheap way to avoid paying taxes on your options until you sell the shares later. And then you're paying the long term capital gains rate on cash earned, instead of short term capital gains on a volatile stock which could easily go down in value.