The main thing is to avoid Holy Week (the week before Easter, which varies from year to year) as everything gets booked up, prices rise and places become very crowded. Otherwise, you can have an enjoyable visit at any time. The dry season, during the amihan or north-easterly monsoon, is in winter - roughly, November to end of April - unless you go to the east coast when the rainy season is between December and March. However, since the Phillippines are generally very hot and humid, many visitors prefer to visit during the winter months anyway, even in rainy areas. The summer, especially early summer around May and June, is too hot for some - temperatures get close to 40 degrees and the humidity is exhausting. On the other hand, from June to September is the cheapest time to visit, and if you pick your area carefully you can find very pleasant weather.
You can find more information here.