2.8 is a larger aperture (Small # = Big Aperture). I larger aperture lets in more light, and therefore lets you use a faster shutter speed.
2.8 is one stop "faster" that f4, therefore your shutter speed will double. Is f/4 + 1/500th was your exposure, then 2.8 + 1/1000th would be the same exposure, but with a faster shutter speed.
The difference between 1/500th and 1/1000th is significant.
You can achieve the same exposure (general level of brightness) with many different combination of controls.
Exposure = ISO+Shutter+Aperture
They work together.
So, all of these exaamples would give you the same exposure, but different effects.
1/125th + f/8 + ISO 200
1/250th + f/5.6 + ISO 200
1/500th + f/4 + ISO 200
1/1000th + f/2.8 + ISO 200
1/2000th + f/2.8 + ISO 400
1/4000th + f2.8 + ISO 800
Fast shutter = Less Blur
High ISO = More Noise (Ugly Grain)
Bigger Aperture (Like 2.8) = Sharp Subject, Blurry Background
Smaller Aperture = Sharp Subject and Background
And that's just getting started, lol.