It doesn’t really matter what the overall size of a sensor is, it is the size of the photosites that matter. The area of the photosite affects how much light can be gathered. The larger the area, the more light that can be collected, resulting in a greater dynamic range, and potentially a better signal quality. Conversely, smaller photosites can provide more detail for a given sensor size. Let’s compare a series of sensors: a smartphone (Apple XR), a MFT sensor (Olympus E-M1(II)), an APS-C sensor (Ricoh GRII) and a full frame sensor (Sony A7 III).

The surface area of the photosites on the Sony sensor is 34.93µm², meaning there are roughly 3× more photons hitting the full-frame photosite than the MFT photosite (11.02µm²), and nearly 18× more than the photosite on the smartphone. So how does this affect the images created?
The size of a photosite relates directly to the amount of light that can be captured. Large photosites are able to perform well in low-light situations, whereas small photosites struggle to capture light, leading to an increase in noise. Being able to capture more light means a higher signal output from a photosite. This means it will require less amplification (a lower ISO), than a sensor with smaller photosites. Collecting more light with the same exposure time and, therefore, respond with higher sensitivity. An exaggerated example is shown in the figure below.

Larger photosites are usually associated with larger sensors, and that’s the reason why many full-frame cameras are good in low-light situations. Photosites do not exist in isolation, and there are other factors which contribute to the light capturing abilities of photosites, e.g. the microlenses that help to gather more light for a photosite, and the small non-functional gaps between each photosite.