While Marc prefers the pricey Mindjet MindManager I've been using the relatively spartan FreeMind for some time now, and include it on the Cratchit.org Small Business PowerPack (which is due for an update).
So now you're thinking, “What the heck is mind mapping software,” aren't you? OK, I'll take a stab at a quick definition. OK. I cribbed the following from my own write-up in my recommended software list. That's because I don't like to write the same stuff twice. If you can't plagiarize yourself, what good are you? On with the explanation.
Think about an outline. Everything sort of branches off of the single root “node” (a node is where it branches). The problem is, when you're looking at a complicated outline sometime after you've built it, it's not immediately clear which items branch directly off of the root node and which branch elsewhere. When you're looking at a certain level, then you miss the “relatedness” of the items because they're visually too far away from the previous level. Mind maps indicate the relatedness of the data in a very visual way by discarding that linear treeview for a more organic-looking structure. It's possible to do some of this with a collapsible outline editor, which is what, “back in the day” (the mid-1980s), we used to call a “thought processor.” It still gets pretty messy, and a mind mapper can clear that up.
Normally I have rule of thumb: I consider any software doomed if you have to have to take a class to understand it. Now, every definition I've seen of mind-mapping -- even at http://www.mind-mapping.co.uk/ or on Tony Buzan's website (and Buzan originated the stuff in the first place) -- fails miserably in the definition and seems to indicate that you need a course in how to do it. In fact, these people charge serious money to conduct such classes. You'd think that if they understood it themselves, they could explain it better than that. (Read Tony Buzan's definition.) I'm with Albert Einstein:“You never truly understand a thing until you can explain it to your grandmother.”
I was ready to apply my rule of thumb and discard this software until I realized that the people pushing the concept commercially and academically do understand the product. They're simply over-educated and over-familiar with it to the point of having lost connection with their audience. They've lost the communication skills necessary to explain their concepts to those who don't yet have their peculiar vocabulary.
A mind mapper is basically an efficient outliner. Conceptually it's the same thing as the treeview list of files and folders you see in your Windows Explorer, only you have great freedom in positioning and labeling the content. And the items can be all over the place, not just in a tree. As such, you get a much better visual representation of where the concepts came from and how they relate to each other. Once you figure that out, mind mapping becomes extremely useful with no further explanation.
Here's what a mind map looks like. It's an actual map that I used to design and track the construction of a project. The process is simple. As you think of features, you add them. If they break down in to smaller components, you list those. If you have a bunch of features that seem to be related, you drag and reposition them so they branch off of the same idea. You don't have to think of everything at once: you just keep shuffling and adding to the map as you think of things, even as the project progresses. Lots of detail isn't necessary, either. You just get things down to the self-explanatory level. On this project I used the icons to track which components were completed or in work. For a small project that's really most of what you need in the way of project management tools. I build software, but you might prefer to use it to plot that detective novel you're writing.
By the way, here's the same map as imported by MindMeister. As you can see, different tools look different, but the concepts are the same. (Though MindMeister did not import my icons, you can add them back in).
If you want to get your thoughts organized, I recommend Freemind, but find what you like. For collaborative work it looks like MindMeister will be just the thing.