A pixel (short for picture element, using the common abbreviation "pix" for "picture") is one of the many tiny dots that make up the representation of a picture in a computer's memory. Each such information element is not really a dot, nor a square, but an abstract sample.
With care, pixels in an image can be reproduced at any size without the appearance of visible dots or squares; but in many contexts, they are reproduced as dots or squares and can be visibly distinct when not fine enough. The intensity of each pixel is variable; in color systems, each pixel has typically three or four dimensions of variability such as red, green and blue, or cyan, magenta, yellow and black.
The term resolution is often used as a pixel count in digital imaging, even though American, Japanese, and international standards specify that it should not be so used, at least in the digital camera field. An image of N pixels high by M pixels wide can have any resolution less than N lines per picture height, or N TV lines. But when the pixel counts are referred to as resolution, the convention is to describe the pixel resolution with the set of two positive integer numbers, where the first number is the number of pixel columns (width) and the second is the number of pixel rows (height), for example as 640 by 480.
Another popular convention is to cite resolution as the total number of pixels in the image, typically given as number of mega pixels, which can be calculated by multiplying pixel columns by pixel rows and dividing by one million. Other conventions include describing pixels per length unit or pixels per area unit, such as pixels per inch or per square inch. None of these pixel resolutions are true resolutions, but they are widely referred to as such; they serve as upper bounds on image resolution.
Below is an illustration of how the same image might appear at different pixel resolutions, if the pixels were poorly rendered as sharp squares (normally, a smooth image reconstruction from pixels would be preferred, but for illustration of pixels, the sharp squares make the point better).
Resolution in various media
DVDs have roughly 500 lines (or TV lines, or lines per picture height).
High definition television has 1,080 lines.
35mm movie film is scanned for release on DVD at 1080 or 2000 lines as of 2005.
35mm optical camera negative motion picture film can resolve up to 6,000 lines.
35mm projection positive motion picture film has about 2,000 lines which results from the analogue printing from the camera negative of an inter positive, and possibly an inter negative, then a projection positive.
Newer films are scanned at 4,000 lines, called 4K scanning, anticipating any advances in digital projection or higher resolution in flat panel display.