As you can see, the leaves are gradually eaten by some gray/dark dry blight. I have absolutely no idea what it is.
That might well be slug or snail damage - given there's lots of leaf litter laying around your plant, you've created a perfect environment for slugs to hide beneath during the day, and then appear at night and snack on your basil. If you want to confirm that's the problem, go out with a torch at night, especially a damp night, and see what's around.
Clear away the plant debris and try using whatever slug/snail bait you prefer to protect the plant.