When you partake in something, you join in, like when you partake in the three-legged race and bobbing for apples at your town fall festival.
The verb partake is almost always followed by the word in, and used in a somewhat formal context. You partake in whatever activities you participate — or take part — in, like when you partake in a backyard football game or partake in your family's holiday cookie making party. If you get a share of something, you also partake of it, like when you partake of the delicious buffet at your cousin's wedding.