This is just a leaf snapped off mom's violet. They can also be cut with a sharp knife. Place in a small cup and keep the stem covered with water until you see root shoots starting. This step can take a couple of months.
Once the roots start put the leaf into some potting soil. Do not cover too deep-no more than 1 inch of stem in the soil.
Wait for the baby violets to start growing. This one is almost ready for splitting. When they get a little bigger, take them out of the cup and pull the babies off. Usually the babies are easily separated once you crumble most of the soil off. Most of the time you get 2-4 new plants off one leaf. You can repot the old leaf if you want more babies of the same type.
Newly potted baby violet! This is just in a dixie cup for now until it gets big enough to warrant a regular pot.