iconkeyboardmacoswindow-manager
Some Mac applications have this button in the upper right. What is it called? Is there a keyboard shortcut for it?
In the case of MacVim, the button toggles the toolbar of colorful icons you see on the left. Saves some space on the screen. Is that what the button does in all applications?
SizeUp is exactly what you need:
SizeUp allows you to quickly position a window to fill exactly half the screen (splitscreen), a quarter of the screen (quadrant), full screen, or centered via the menu bar or configurable system-wide shortcuts (hotkeys). Similar to "tiled windows" functionality available on other operating systems.
I use AccessMenubarApps which works on the basic principle of temporarily replacing the current menubar with a shorter one to allow all the menubar icons to be visible. It can be accessed by clicking on the icon, via mouse gestures, or a configurable hotkey.
Best Answer
Yes, it toggles the toolbar in all applications. In many applications, it's shortcut is Option+Command+T, but this is not true for all (Preview uses Command+B).