Pixels: A Pixel is an itty bitty tiny spot of illumination of a display screen, if you put many of them together you get an image. It is also talked about in print quality as in pixels per square inch and square centimetre (Pixel Density). We also see Pixels used to describe camera sensor quality as in megapixels that a camera can achieve.
Each pixel can only be one colour at any given time. You can see the individual pixels unless you get up really close or unless the resolution of a screen or print is small. In these cases you start to see the square edges of the pixels. This is called being pixelated.
When we talk about screen resolution we talk about pixels that are illuminated on the screen. The more pixels you have the better the image looks.
When printing pixels per inch (or centimetre) we are talking about spots of colour being transferred to paper. It is not pixels at all but Dots per inch. Printers reproduce an image by mixing four colours in dots that then make up the images. DPI measures their density. If you print an image the pixels will change in size depending on the size that they are printed at, so the printer will increase the size of a pixel as it increases the size of the image.. If you have a high quality image but you print it billboard size then look closely at it you will be able to see the individual dots of ink. If you have a low resolution image and try to print it, the printer will see the image but it will look soft and not good quality.
The other problem can be that a resolution of 72 and 300 might look the same on a computer screen but will print very differently.
The best advice is to always edit your image at the best quality that you can if you are planning to print enlargements of them. And after all, we should as photographers want to see our images end up as printed products to be enjoyed more than just flicking through them on our web sites, phones or computer screens. But that is a whole other blog post ;-).