Looks like you’ve got 1x6 boards as your fascia which are probably pine, cedar or something similar depending on your region with plywood under the soffit. This is how they are traditionally done.
Nothing wrong with this but they do require maintenance. You’ll pay a premium these days for solid wood which is why most builders and budget conscious people pick cement and man made products.
This honestly looks like it is decent shape still and is just due for some maintenance. But pictures can be deceiving. Poke it with a screwdriver. If it’s solid then strip and repaint. It may take a little more labor if a board needs replacing but I personally favor repairing something that is fixable.