This is one of those little things that I'm a little embarrassed to just have discovered after working in .NET for four years, but I'll just go over to Leon Bambrick's "You are not inadequate" blog article for a quick reminder that it is a-okay not to be familiar with every single class and class member in .NET. It's totally a productivity gem, not really earth-shattering.
I've never fiddled with this attribute, but had assumed that DefaultProperty would bring me back to the good ol' VB6 days of letting your UI know that obviously, the most common property I want when I'm inspecting a TextBox is the Text value and I could just set the DefaultProperty to Text and go on with my ultra-Lazy habits. But reason intrudes and reminds me that I would then be passing a TextBox object where a string is expected. Or if I wanted to use Height as the default, I would be passing a TextBox type where an Integer is expected. So I finally took a look at this attribute today and was very happy when I realized what it was best used for.
When you use DefaultProperty on a control, the property that you assign becomes the design time default property of the control. Therefore, when you drop the control on the design surface, that property automatically gets focus in the properties window. Note that this is only going to happen in this instance, not later when you select the control again.
This becomes truly dreamy even in a very simplistic example such as creating a new Label control with the DefaultProperty set to "Text". This label does nothing else to the regular label.
<DefaultProperty("Text")> _
Public Class LazyLabel
Inherits Label
End Class
In VS2005, this shows up in the Toolbox under the components tab for your project. My project is called "Attributes".

And the tiny little lazy thing that made my day is that now when I drop a label onto a new page, I can just literally type in the Text value of the label without having to go over to the properties window and select the Text property. Drag, drop and type. Ooh let's do that again. Drag, drop and type. Very gratifiying! And 99% of the time, this is all I want to do with a label anyway! :-)