There are two ways to create an image to be viewed on a computer - vector and raster. Raster is what most people are familiar with - a more common term is *pixels*, that is, the tiny colored squares that, when put together, create an image. The smaller the squares, the sharper the image. That is what is known as *resolution*. If you've worked with Adobe Photoshop, you are aware that resolution is an important calculation to make before you create any artwork.
An image created with vectors is independent of resolution. If you create a drawing in Adobe Illustrator, it can be output to any resolution you want. The best way to describe vectors is that they can be enlarged indefinitely without any loss of sharpness. That is because a vector image is not created with pixels at all. It is created with a series of points that are tied together like wires. When those wire forms are completed, they can be colored, textured, and reshaped easily. When you draw something in Adobe Illustrator, you never have to think of resolution. And I like that!