I've sold a few books on proposition, and I remember when I first heard about that I was amazed. You always hear the advice "finish the book before you start to shop it around." But sometimes the idea is so original you're not quite sure if it will interest anyone, and in that case it might be better to approach a publisher with the idea to see if there is any interest. Another reason could be just the opposite -you have a great idea you know will be a hit, and you want to get to work on it as soon as possible, so you shop it around first.
Another reason for writing a propostion can come from an agent, an editor, or a publisher. I had my editor suggest a book, we wrote up a proposition, and it was contracted before it was written by EC. Changeling Press were launching their line and wanted something original, so I proposed an m/m sci-fi romance, and they contracted the series on proposal. Right now my agent has an idea she thinks would be right for me, and she wants me to write a proposal for it.
What is a proposal?
It's a synopsis and about three chapters. It can include a full outline (or not). Some authors are pantsers and couldn't outline to save their lives - but no problem, most publishers and editors have worked with authors of All types and don't ask for outlines very often.
So what am I doing now? Well, I finished the synopsis and I'm writing the first three chapters of the book. I'm writing a rough draft - no worries about making it perfect yet - what my agent is looking for is character developement and mood.
I'm also doing it in first person POV, which is actually my favorite POV to work in, and I'm hoping it will work for this story. I have a little research to do right now - I'm setting the story in an actual town, and I need to get the street names right. Luckily it's a place I've been to many times, so I know more or less how it looks and what the surroundings are like, but I am a perfectionist...and besides, research is another name for procrastination, and we all know that I am the Queen of Procrastination!!