A vexel is a style of digital art that uses block shapes of color to create an image.
For a long time these images were always referred to as "vector art" regardless of whether they were actually vector or not. The word "Vector" refers to "creation of digital images through a sequence of commands or mathematical statements that place lines and shapes in a given two-dimensional or three-dimensional space" (*Whatis). To put that more simply, vector art is something made in a vector program (eg. Flash, Illustrator, Freehand) and can be resized without any kind of pixelation or quality loss. Vexels on the other hand, can be raster or vector images. Vexels are often seen as cartoon versions of an image or photo.

You can make a vexel in any graphics program, it doesn't matter if it's Illustrator or Photoshop, vector or raster, a vexel is nothing to do with the format.

What is the difference between vector and vexel?
That is like comparing apples to.. elephants. Vector is a type of art, it doesn't have to look like anything in particular. Just like "painting" doesn't have to look like anything in particular, it is just a medium. Vexels on the other hand are a style of art - usually seen as a cartoon version of a photo (although a photo is not always used).

Are airbrushes or digital paintings vexels?
No. The main defining feature of a vexel are the clean block shapes. Airbrushes or paintings do not have block shapes.

What about gradients?
Sometimes. If the gradient is well defined and can still be seen as it's own shape then yes.

Is anything made in a vector program a vexel?
No. Programs like illustrator have features such as the gradient mesh tool which allow people to create images which are nothing like vexels. Remember, the main defining factor of a vexel is the clean block shapes of color.

Is it just tracing?
For some, vexelling is tracing over a photo. For others, it is using a photo as a base and manipulating it in such a way that it is not recognizable. Some people draw their vexels from scratch or from a sketch they've done. For some people, duplicating a photograph is looked down upon, others find it admirable.

Does a vexel have to be of a person?
No. It can be of anything, it can even be an abstract piece. You will find many of the vexels on this site are of female people - this is for a few reasons:
Most tutorials feature females, so that is what people learn
They are easy to customize and make your own with different hairstyles, makeup, clothing etc.
They are beautiful and people want their work to be beautiful too.

I used a filter, is it a vexel? It looks like a vexel!
No. Simply using a few filters such as posterizing, live trace, trace bitmap or cut out does not make your image a vexel. These images are easy to pick out from real vexels as no program can give attention to detail like a human eye can.

Where did the term Vexel come from?
Seth came up with the term. It is a mixture of "Vector" and "Pixel" - meaning a pixel based image in the style of a vector. You can read the text from the original thread here.

How do I make a vexel?
Check out the vexel tutorial listing.

I use vector therefore I and my art are better.
No, if you think that, you are not grasping what vexel means. A lot of vector art is still vexel art and vice versa.