Cherry blossom season in Japan is nice but short. Once the trees have started to bloom, it is over within a week. As a result, the parks gets very crowded with people picnicking under the trees.
Japanese word for cherry blossom is 桜（さくら / Sakura）. There are a lot of varieties with everything from white to pink.
In Japan, the season is end of March to beginning of April (of course, depending on where in the country you are).
You can find the cherry blossom forecast at the Japanese Meteorological Agency. For 2016, the forecast is available at the following link. This is not available in english, but if you like to find the latest one, go to the Japanese page, and search for 桜.