A picture is worth a thousand words, here. This is a Twin Lens Reflex camera:
The two lenses are linked together so they focus as a set (either the whole front panel moves, or the lenses are linked by gears so that they turn together to focus). The top lens — the "viewing lens" — has a mirror which bounces the view to the ground-glass viewfinder. The bottom lens — the "taking lens" — has a direct path to the film.
This was a big innovation, because previously, the photographer would focus, and then carefully replace the viewfinder's ground-glass screen with the recording media (glass plate or film-holder or whatever). You could have a twin-lens design which doesn't use a mirror, but the mirror allows for a more convenient viewfinder location and a much more compact design.
If you're used to SLR cameras, it's easy to assume that "reflex" means "the complicated thing where the mirror dodges out of the path of the film right at the last minute", but this isn't it. It actually refers to the mirror itself; from Merriam-Webster, this is a different use of the word:
a archaic : reflected heat, light, or color
b : a mirrored image
c : a copy exact in essential or peculiar features
So, Single Lens Reflex shares the "reflex" part, but has a Single Lens in contrast to Twin — with this design mirror moves out of the way, allowing the same lens to share viewing and taking duties. There are advantages and disadvantages: moving the mirror is complicated, can shake the camera, and there's a blackout right as the photo is taken. SLR cameras were actually invented very early on, but didn't really come to dominate until technology had advanced enough to minimize these disadvantages,
"Single lens" can also apply to other camera types, like those without a reflex mirror. While terms like "mirrorless" are more common, Canon refers to the M series as single-lens non-reflex — one (interchangeable) lens, no mirror.
There is also sometimes confusion about what exactly a "single lens" is — isn't that a single piece of glass, like a magnifying glass? Not necessarily! There are three types of things we call "lenses": simple lenses, compound lenses, and complex lenses.
A compound lens includes multiple simple lenses ("elements") next to each other and a complex lens includes groups of lenses (compound or simple) with space between them. So, "Single lens" can mean a single simple lens or a single complex lens. In photography, we almost always mean the latter.