It would be easier to retype the text, then apply an effect to the text layer using the layer effects plug-in http://registry.gimp.org/node/186 , then delete the background layer, then you could export the image as a png. It will need to be a png, because jpegs don't support transparency.
If your banner is simply going to have photos behind the logo, like a solid background, then you could get away with using jpeg if you don't need actual transparency in the image.
If you can't retype the text, for example if you don't have the font, then you would have to make a selection around the the black text, invert the selection, add an alpha channel to the layer (to enable transparency) - then erase the background. Then export as a png. Obviously the problem here is how good it looks will depend on your skills to select precisely around the text, so that when you erase the background no white pixels are left. You could use automatic selection tools like the select by colour tool, adjusting the threshold in the tool options to get it as accurate as possible, however it is going to be harder to get a decent result than if you just retyped the text. Chances are you are going to get something that ends up looking very amateurish.
To answer your other query, the word "rasterizing" isn't used for extracting an image from a background. Rasterizing is when you take an image that is not already a raster image, for example a vector image, a text layer, or a layer mask, and render it as a raster image (made of pixels). Extracting could indeed be termed a type of rendering, but it can't be called "rasterizing" - since the image is already made of pixels.