What Is a Writing Partner?
A writing partner is another writer that you are friends with. The two (or more) of you talk to each other about writing and your stories and encourage one another. A famous pair would be J. R. R. Tolkien and C. S. Lewis, who were both part of the Inklings.
What Are They Good For?
My writing partner is my sister. I think she is a great one. A partner helps you with your writing. We talk about plots, give each other things to read over, and help each other with characters. That's only a small part. We discuss various things we've read (like should you only use "said" or can you use other words like "whispered" or "yelled"). We tell each other about great books we've read or terrible ones and what we'd do better. It is fun and helpful. While talking, both she and I have gotten cool new ideas for stories. One we even turned into a story that we are currently writing together.
Should I Have One?
I would definitely recommend finding a writing partner. As I said, it's a good idea for any writer. Writing is often a lonely process and having someone to talk reduces that alone feeling. But how can you find a person to write with? It's not hard. Do you have a friend that writes? Ask if they would like to get together and talk about writing once in a while. Maybe you can have weekly meetings. Or sometimes you can connect with people online, like through the NaNoWriMo website and become friends that way.
I hope this helps you and that you can find someone to write with.