The biggest feature of literary writing is that it is very often based on imagination, ideas and unreal things. As the name suggests, the language used in literary writing is a rich one. The writer uses rich words, poetic devices other language enhancing elements to give the written piece, a good taste and appearance.
Examples of literary writing - Fiction, Poems , Plays etc.
Non-literary writing is what we often come across in our daily life. It can be instructions, short messages etc. which are written purely for the purpose of informing someone or are business and work related. They don't have the writer's imagination sewn into them.These lack in rich language and words and are related to the reality only.
Examples- Instructions given by your teacher, A short message informing your sister about her phone call, a short note telling about progress at work. etc. These are all non- literary writings.