The caption bar of a Windows application window display icons in 16x16 pixels. The Alt-Tab list, however, shows icons in 32x32 pixels. It uses the same icon as is set for the window. If you only set a 32x32 one, the caption bar has to scale it down, which tends to look ugly as it uses nearest-neighbor interpolation. So how does one support both?
The answer is the ICO file! It supports embedding multiple icons in one file, typically the same (or similar) icon in various sizes and, less commonly, color formats.
Browsers, Windows, and others are typically designed to smartly use the appropriately sized variant within a given ICO file. So the answer is to have an ICO file with both sizes (or more) inside. The result is that the caption bar correctly uses the 16x16 version and Alt-Tab uses the larger 32x32 one.
The methods for saving an ICO file with multiple icons inside varies from program to program. However, GIMP can easily do it (and it's free). The trick is to have your variously-sized icons as separate layers. When you go to save it as an ICO file, GIMP will prompt you with the ability to set the size and color format of each layer. A good tutorial, with images, can be read here.
If anyone has any links or suggestions for creating multi-icon ICO files in other programs, feel free to add them. Also, I'm unsure if the Visual Studio built-in image editor can do it or not — I've rarely bothered with it.