When you see a woodpecker, they are typically clinging onto the bark of a tree or branches, usually using their tail to prop themselves up. This position would typically put a lot of pressure and wear on their longest tail feathers. Because of this risk of increased damage to these feathers, they have a special adaptation. These tail feathers come to a point and are extra stiff to allow them to overcome this extra wear and tear that they are subjected too.
In addition, you will probably notice that most woodpecker tail feathers are black, containing the pigment melanin. Melanin not only provides color to feathers, but also adds strength to them, making them more resistant to wear and damage. This is the same reason you may see many bird species with black primary feathers.