A looper is a recording device allowing you to record your guitar playing, and then play it back as a loop. The “bigger” the looper (read: the more memory space it offers) the more recording time will be available, making very long loops and/or lots of overdubs possible. Looping originally started in the Sixties with tape machines and tape echoes, which is why looper pedals are usually found in the same product group as delay pedals.
Loopers have become an important tool for buskers and solo artists. It’s relatively easy to achieve impressive results, when soloing over a (self-recorded) looped backing.
Of course, you can also run your loops through other effects. Try running a loop through a delay pedal for some spaced out soundscapes. Or add distortion to some parts, while keeping the rest clean. The biggest loopers are crammed with features, basically putting a whole recording studio at your feet. Go where your imagination takes you!