On antebellum plantations in the Old South, slaves often were given the days between Christmas and New Year's off (apart from a few necessary tasks like milking the cows). I don't think they want to make a connection between that tradition and Kwanzaa.
The pagan Romans celebrated the birthday of the sun on December 25, which was then the date of the winter solstice (when the sun was about to start moving northward in the sky). The early Christians did not know the actual date of Jesus' birth so they picked December 25 to put a Christian meaning on the day of the pagan feast.
Africa is in the southern hemisphere so it is summer at the end of December. Crops probably are being harvested at that time of the year.