The entrance pupil "collects" light on behalf of the entire optical system and hence determines the "speed" of a lens.
In technical terms, the entrance pupil is the image of the aperture opening and thus is a virtual quantity. It can actually be larger in diameter than the lens itself. Not many examples of that kind exists, but some for sure do and it is a little unnerving to look into such lenses and realise the "hole" is bigger than the lens
Further worth noting that the nominal aperture (thus "speed") of the lens always refers to infinity focus, whether or not the lens actually can reach infinity.
A well-known example is the famous Repro-Nikkor 85 mm f/1. It has an entrance pupil of 86 mm (it is actual focal length is, not coincidently, also 86 mm) and this is an f/1 lens. It is also perfectly symmetric so its pupil factor is 1 too. However, it is used at m=1 (or life-size 1:1 magnification), so its effective aperture at that magnification is f/2. Depth of field corresponds to f/1 though.