When your friend scribbles a note to you and you can’t figure out what it says, it’s because her handwriting is illegible — it’s unreadable.
The adjective illegible is often used to describe handwriting, because people tend to have their own styles and sometimes write in a pretty messy way. But it can also refer to printed words that are faded or for some other reason difficult to read. If you leave a book open in the rain, the print will probably become illegible. If you’re walking in an old graveyard, the writing on the tombstones is often illegible.