Cursive is a style of writing in which all the letters in a word are connected. It's also known as script or longhand. When the third-grade students learned cursive writing, they were excited to find that they could write entire words without lifting their pencil from the paper.
Cursive comes from the past participle of the Latin word currere, which means "to run." In cursive handwriting, the letters all run into one another and the hand runs across the page, never lifting between letters. Every time a document asks for your signature at the bottom of a document, you are meant to use this flowing cursive writing style.