Do your own toe nail grow their nail?

No, toenails do not grow their own nails. Toenails are made up of a protein called keratin, which is the same protein that makes up the outer layer of your skin and hair. When this keratin is produced, it forms a hard layer on the surface of your nail, which is then pushed out from your nail bed by new keratin cells growing behind it. This is why toenails grow outwards and not upwards. So it's not the nails themselves that grow, but rather the new keratin cells pushing them out that give the appearance of growth.