SVG is short for Scalable Vector Graphics. It is a graphic format in which the shapes are specified in XML. The XML is then rendered by an SVG viewer. Today most web browser can display SVG just like they can display PNG, GIF, and JPG.
Internet Explorer 8 (and earlier) users may have to install the Adobe SVG Viewer to be able to view SVG in the browser. IE 9+, Chrome and Firefox all support SVG natively.
SVG is for 2-dimensional vector graphics. For a 3-dimensional format lookup X3D.
If you are not sure if SVG is right for you or your project, take a quick look at the SVG Examples page to get a quick overview at the capabilities of SVG.
SVG Tutorials as Video
I have a video version of this text here: