The focal ratio of a lens (sometimes referred to as Aperture value or Av, but more commonly as a focal ratio or f-stop and written using the short-hand f/__) is really the focal length of the lens divided by the diameter of clear aperture.
In other words if a lens had a physical aperture opening with a 25mm diameter and was had a focal length of 100mm then the the focal ratio would be f/4 because 100 ÷ 25 = 4. If you increase the focal length to 200mm but do not change the physical aperture size then it becomes 200 ÷ 4 = 8 ... so now it's f/8. In this example the only thing you deliberately changed was the focal length but the focal ratio changes as a side-effect of the math.
Some lenses employ optics that are able to maintain the focal ratio even while you adjust the focal length (and these tend to be more expensive lenses.)
Knowing that focal ratio is the focal length divided by the clear aperture diameter, this also means that "long" lenses that have "low" focal ratios will probably be very heavy because the low focal ratio requires a large physical diameter (relative to the focal length of the lens). That means each glass element inside the lens has a much larger diameter ... which also means they are thicker and that means they are are heavier.
You might wonder why focal ratios are used instead of just stating the physical diameter of the aperture. It turns out that for purposes of determining how much light will be delivered to the sensor, it is the ratio which matters. e.g. if a lens has a 25mm aperture diameter you really don't know how much light will be delivered to the sensor unless you also know the focal length.
I use a thought experiment of a tunnel in the side of a mountain. If the tunnel diameter is 20' across and you stand at the entrance to the tunnel it will be quite bright because light from many different angles can reach you while you are at the tunnel entrance. As you got deeper into the tunnel, the angle of light necessary to reach deep inside becomes narrower and narrower and the consequence of this is that it gets darker and darker the farther you go. Focal ratios work like this.
This means when you use a light meter to take a meter reading you do not have to tell the meter anything about the focal length of your lens... it can recommend exposure settings based on the focal ratio regardless of the actual focal length.
One other thing to notice... those numbers used in the f-stops... are actually powers of the square root of 2. (the square root of 2 being approximately 1.4 when liberally rounded)
This is because each time you increase the diameter of a circle by that factor (1.4 ... actually by the square root of 2 if you want to be precise) then you will exactly double the area of that circle. That means twice as many photons can pass through that area. The area of the circle is π * radius^2. If you increase the radius by 1.4 (or √2 to be precise) then you will exactly double the area of that circle.
Here is a table I created showing the powers of the square root of 2 ... from 0 to 9. Notice that only the power is changed on the left and on the right you get list of whole f-stops. Each whole f-stop decreases the amount of light by exactly half. f/1.4 allows half as much light to pass through the lens as compared to f/1.0. f/2 is half as much light as compared to f/1.4... and so on.
Camera manufacturers round values used in photography because use of precise (non-rounded) values wont change the exposure in a noticeable way (i.e. hundredths of an f-stop wont be noticed) and it makes the values easier to remember.