(For a video version of this frequently asked question and answer, click this link.)
After Effects must convert imported vector graphics to bitmap (raster) graphics. By default, this conversion (called "rasterization") happens once for a layer, and it happens before transformations, like scaling. This means that scaling such a layer up is really scaling a bitmap image, and that can expose jagged pixelation.
You can tell After Effects to rasterize after transformations like scaling, and to do so once per frame, to ensure that each frame is as crisp as possible. Just click the Continuously Rasterize switch for the layer.
This is only an issue for imported vector graphics (from Illustrator, SWF, EPS, and PDF files). Vector graphics created in After Effects, like text and shape layers, are always continuously rasterized.