Something that's nonexistent doesn't really exist. When your cat hisses at her reflection in the mirror, she's attacking a nonexistent enemy.
The adjective nonexistent describes something that's not real. Your nonexistent problems are only in your imagination, for example, and you may pretend to answer a nonexistent phone call to avoid an awkward conversation with an acquaintance at the post office. The word existent is at the heart of nonexistent, with its root of existence. They all come from the Latin word exsistere, "to come into being, to appear, or to be."