What is the difference between a vector and raster?

Another one of the most common terms you hear in the GIS field are the words "Vector" and Raster" images.

What is the difference? I'll try to keep at as concise as possible. 

Raster:

A raster is a set of pixels (dots) arranged in a grid, where each pixel contains a unique value. The unique value can contain any kind of information. To understand it easier, think of each pixel containing a value which pertains to a color. So therefore, each pixel will be a color. Now think of these pixels arranged in an organized grid, where each pixel contains a color, when you look at the grid from a distance, you will see a collection of colors. 

Below is a grid, with each pixel containing no color, or blue. You see the arrangement makes up an image of a fish. 

 

Now look at the image from a distance, it looks like a fish. Bring your face closer to the screen. If you make the image larger, it is going look a little distorted. This is one of the disadvantages of raster images. Because everything is set in pixels, if you are to blow up the image from a small paper to a large, it will look awful. 

Vector:

A vector are mathematical sets of information arranged to make up the image intended. To make it simpler, let's say you have an equation that makes up a line. Imagine you manipulate each equation to make sets of lines curve the way you want. These lines collected makes an image. 

Since the line is made of a mathematical equation, if you wanted to increase your image size by 10 times, so from a 8x11 paper to 60x42 inch, the image will look exactly the same. This is because the mathematical equation redraws itself on the paper, no matter the size. The proportion is still the same.