What are sprites and why would use them? How do you go about creating them? What are possible alternatives to sprites?

Sprites are essentially multiple images combined into one. Performance is the reason that they are used. Generally speaking, the slowest thing a website can do is request a resource. The fewer requests a site needs to make, the faster it is. Fast = good. Combining what would be many requests into one = good.
Asking how they make sprites would just seal the deal that they are actually very familiar with them. Manually creating sprites is certainly a possibility but it isn't very efficent. There are helper tools like SpriteCow and SpriteMe, Spriting with Compass, or Grunticon. It's always interesting to hear a real workflow approach.
Sprites are raster images. When asking about alternatives, good answers might be related to the fact that sprites are often for icons and icons often don't need to be raster. SVG Stacks, Icon Fonts, Unicode…