The short story is that Phuket has a fairly typical tropical weather pattern.  Two seasons really, a hot season, which is fairly dry and a rainy season, which is a little cooler (though it never really gets cold).  Check the chart below for exact totals.  Some like the rainy season because it cools the weather down a little.  The rain will rarely change your daily plans.  Typically (if such a thing exists), there is a good afternoon thundershower (20-60 minutes) during the rainy season and a good hard rain in the middle of the night.  But, the island does get the occasional 2-3 day storm, which you might not enjoy if it is in the middle of your vacation.

Here's a chart of the weather from Alex Malcolm - click on the chart to go to his website and get even more detailed information, including day by day reports.

The information below is compiled from Phuket International Airport and reported via the National Weather Service: