Pixel-based ("raster") formats break the image up into a limited number of points (pixels), where each pixel displays a given color. If the pixel density is high enough, our eyes won't be able to discriminate between the individual pixels, giving the appearance of a smooth image. However, as the density decreases (i.e. via zooming in), such that fewer pixels will be used to fill the same amount of space, the pixels will become more obvious (the image will appear "blocky"). Vector graphics, on the other hand, consist of specifications for paths through the image space (like, say, a line or a curve). Thus, you can choose any section of the image and any level of zoom, and the computer will re-compute and re-draw the paths. This allows the image to appear smooth no matter the zoom level.
The advantage of vector graphics is their persistent image quality. However, they have the disadvantage of being computationally heavy: zooming and panning an image requires a recomputation of the view of every path. Also, many graphical effects (blurring, distortion, etc) depend on a rasterized image since they work via pixel-based calculations. Also, vector graphics should require far less disk space than a high-resolution raster image. On the other hand, some types of images, such as photographs, are simply more practical in raster formats.
As for comparing text written in Gimp and Inkscape, I'm not 100% sure how Gimp works, but when you initially enter text in a text box, it might be vector-like. I bet if you first rasterize the image with the text (i.e. export it as a bmp) and then compare the bmp with the image in Inkscape, you'll see the difference.