My simple definition of alpha channel, a colored image has 3 standard channels red,green,blue, the 4th channel is the alpha which allows you to control the opacity or transparency.
If you are interested in a detailed definition of a what is an alpha channel I got one from techopedia.com below:
The alpha channel is a color component that represents the degree of transparency (or opacity) of a color (i.e., the red, green and blue channels). It is used to determine how a pixel is rendered when blended with another.
The alpha channel controls the transparency or opacity of a color. Its value can be represented as a real value, a percentage, or an integer: full transparency is 0.0, 0% or 0, whereas full opacity is 1.0, 100% or 255, respectively.
When a color (source) is blended with another color (background), e.g., when an image is overlaid onto another image, the alpha value of the source color is used to determine the resulting color. If the alpha value is opaque, the source color overwrites the destination color; if transparent, the source color is invisible, allowing the background color to show through. If the value is in between, the resulting color has a varying degree of transparency/opacity, which creates a translucent effect.
The alpha channel is used primarily in alpha blending and alpha compositing.