African witchcraft is not easy to define when you consider there are more than 50 different nations currently making up the diverse population of the continent. Not to mention the thousands of years of history on top of that. Basically, its not really one single topic.
Many traditional African belief systems included different types of witchcraft and shamanism, but the influx of Christian missionaries have wiped out countless indigenous religions. Admittedly, some traditional beliefs considered witches to be evil in the first place but the addition of Christianity has added more negative associations even where there were none originally.
People are still burned for practicing witchcraft in some countries, not because of official law but rather by cultural practice. Aside from these issues, there are two forms of magickal practice that people associate with African witchcraft: Santeria and Vodou.
Most people associate Santeria with the Caribbean, which is accurate but it does also have deep roots in Western Africa. It is a blending of the original Yoruba religion from Africa, with many aspects of Roman Catholicism. This combination of beliefs arose from the slave trade, where Africans were taken to the various Caribbean islands to work. They adapted many Catholic beliefs, particularly the host of saints and created a unique religion that is still practiced there today.
In Santeria, there is a great Creator Deity but it is the Orishas that are directly worshiped. The Orishas are comparable to the Catholic saints, and they often have similar traits and characteristics. For example, Elegba and St. Anthony are closely connected as patrons over roads, transportation and gateways.
Though the saints are similar, the practices are very different from Catholicism. Santeria rituals often involve animal sacrifice along with vibrant dancing and drums. Offerings of food and alcohol are commonly associated with most Orisha.
Though many people call it Voodoo, the more accurate name is Vodun or Vodou. It's a religion similar to Santeria as a mixture of Christian and African beliefs but it has gotten a lot more negative exposure from TV and movies. Vodou came from African with slaves and is primarily practiced in Haiti as well as some African nations.
There is one unknowable Deity figure, Olorun and the lesser spirits who are worshiped and prayed to are called the Loa (or the Lwa). Again, they are similar to many saints but the connection is not as strong as in Santeria.
Rituals in Vodou involve dancing and drumming and there is also sometimes animal sacrifice. Symbols called veves, drawn in various powders are used to call the Loa to the ritual.
These are both examples of African witchcraft, though they do not resemble the Wiccan form of witchcraft very much.