What exactly does the little green "+" button do in Mac OS X?

I hate the default behavior of that button... To make the green buttom actually maximize the window, try either RightZoom or Stoplight.

It's called the "Zoom Button". Defined by Apple as:

A control that toggles a window between its standard state and its user state.

From here.

What I take that as is basically that it's "Standard state" is the window size that the programmer hardcoded into the application. The "User state" is the size you've changed it to.

In document-based applications, the zoom button toggles between the user state and the optimum size for the content. Unfortunately, many applications, such as Firefox and even Safari, don't actually obey this rule.

From the OSXHIGuidelines:

Your application determines the minimum and maximum window size. Base these sizes on the resolution of the display and on the constraints of your interface. For document windows, try to show as much of the content as possible, or a reasonable unit, such as a page.

Your application also sets the values for the initial size and position of a window, called the standard state. Don’t assume that the standard state should be as large as possible; some monitors are much larger than the useful size for a window. Choose a standard state that is best suited for working on the type of document your application creates and that shows as much of the document’s contents as possible.

The user can’t change the standard size and location of a window, but your application can change the standard state when appropriate. For example, a word processor might define the standard size and location as wide enough to display a document whose width is specified in the Page Setup dialog.

The user changes a window’s size by dragging the size control (in the lower-right corner). As a user drags, the amount of visible content in the window changes. The upper-left corner of the window remains in the same place. The actual window contents are displayed at all times.

If the user changes a window’s size or location by at least 7 pixels, the new size and location is the user state.The user can toggle between the standard state and the user state by clicking the zoom button. When the user clicks the zoom button of a window in the user state, your application should first determine the appropriate size of the standard state. Move the window as little as possible to make it the standard size, and keep the entire window on the screen. The zoom button should not cause the window to fill the entire screen unless that was the last state the user set.

When a user with more than one monitor zooms a window, the standard state should be on the monitor containing the largest portion of the window, not necessarily the monitor with the menu bar. This means that if the user moves a window between monitors, the window’s position in the standard state could be on different monitors at different times. The standard state for any window must always be fully contained on a single monitor.

When zooming a window, make sure it doesn’t overlap with the Dock. For more information about the Dock, see “The Dock.”