In the simplest terms, GDI+ is a set of namespaces that provides for the rendering of 2D graphics. For example, GDI+ provides support for colors, pens, fonts, image transformations, and antialiasing. GDI+ contains none of the advanced animation and 3D rendering features found in DirectX.
Notice that I didn't include the phrase "render to the video adaptor" in the preceding paragraph, because the device GDI+ renders to is immaterial. Well, almost immaterial—there are some differences that have to be accounted for between some devices. For example, video adaptors don't have to worry about form feeds, whereas printers obviously do. GDI+ is designed to support almost any graphical display device.
GDI+ originated from the Windows Graphical Device Interface (GDI), which has been around since Microsoft Windows 3.0. GDI+ shares many of the features of its predecessor, but with the .NET Framework class library there have been several improvements, thus the new name of GDI+.