Paganism is best defined by what it is not rather than what it is. Paganism is literally hundreds of things, among them Asatru(worship of the Norse Gods), Kemetic/Netjer (worship of the Egyptian Gods), Native American and Australian Aborigine shamanism, Wicca, witchcraft, Voodoo, Afican Native religion, and too many others to fully list here. A pagan is generally defined as a follower of a nature religion that is not part of Christianity, Islam, or Judaism. The word pagan comes from the latin word for country dweller, and was originally used as a derogatory term by the Romans to describe any country "hick" who was unsophisticated or practiced a non-mainstream religion (and incidentally the early Christians were called pagans by the Romans LOL).
Wicca is then a subset of paganism. Wicca is a word first used around 50 years ago or so to define a type of religion reconstructed from what is thought to have been practiced by witches in ancient times, ie. a belief in the God and Goddess (in all Their many forms and names), honoring the Rede, (An it harm none, do as ye will), the Rule of Three (whatever you put out comes back to you three times), and celebrating the Wheel of the Year (the eight sabbats: Samhain, Yule, Imbolc, Ostara, Beltaine, Litha, Lammas, and Mabon), full and new moons (Esbats) and practicing magick. There are lots of variations within Wicca (the variations are called traditions) based on various interpretations and personal beliefs (I have heard it said that there are as many traditions as there are Wiccans). Some of the more formalized traditions are Gardnerian, Alexandran, Faery, and Celtic, but there are many, many more.