Persuasive writing is such a writing that aims to make an influence on a reader, convince him/her to opinion provided by the writer. It is very common, especially in marketing. Almost all advertisements are samples of persuasive writing.
This type of writing is used when you want to persuade or convince someone to agree with your opinion.  This can be done as an essay or a letter.      Make sure you have specific, logical reasons to back up your argument.  (Don't just write " because it's the right thing to do", or " because it will make the world a better place".)