Vector art is best suited for printing. The vector art is made from a series of mathematical curves, it prints very sharp, and is scalable to any size. The logo you created for business card, can be enlarged to a big billboard and still it looks as sharp as it was on a business card.
Raster images (jpg, tiff, png, gif etc.) are dependent on the resolution. If the artwork enlarged beyond the required ppi/dpi, it looks blurry and pixelated. For printing, required resolution of the file is 270 dpi to 300 dpi.
For websites or online viewing (on laptop or desktop computer) you need 72PPI, tablets support higher PPI. SVG is a scalable format for web but it’s still not widely supported by all the browsers.