White pepper is used to a great extent in recipes for appearance only, usually in white sauces where you might not want dark specks (if black pepper was used). White pepper is milder in flavor than black pepper. You can certainly substitute black pepper for white pepper, knowing that the black specks will show. You may want to start with less black pepper than the white pepper called for and adjust the flavor as you go.
Like spice? Try these recipes that feature white and black pepper.