The crux of it? It increases the low light performance. How? By moving the circuitry that usually shares space on the front of the sensor with photosites to the back of the PCB (printed circuit board).
A sensor uses photosites to gather light (red, green, and blue to make a pixel), and traditionally the photosite would have its circuitry next to it on the PCB. Moving it to the back allows the photosite to be larger, and thus more accurate due to getting a larger sample of photons to make each pixel.
Other ways a manufacturer makes a sensor have bigger photosites, is by making the entire sensor bigger (ie. a phone vs a full frame camera). Or by having a lower resolution, meaning the sensor doesn’t have to be divided up as much into many pixels.
Should you look for a camera specifically because of this jargon? No. All cameras have noise processing whilst recording of some kind, and some cameras do it better despite photosite size. So look at a camera’s image, and see if it suits your needs/budget. Don’t be suckered in by catchwords like “Backlit Sensor” 🙂