A pointed projection has formed where my tooth was removed. What could this be?

Bone. Sometimes after the removal of a tooth a smalll bone piece can work its way out of the extraction site. It is common and usually nothing to worry about. It will take time for your bone to re-model around the extraction site. Call your dentist who can determine if it needs additonal care or not.
Tooth or bone. It could be a piece of the tooth or a bone fragment trying to work itself out. You should return to your dentist to have a look.
Scar. Or possibly a fragment of the tooth left behind. A dental x-ray will answer this for certain; unless it is painful it can wait until your next exam. If it is bothering you, go back to the dentist who pulled the tooth.