Exposure is determined by the sensitivity of the recording medium (film or digital light sensor), the amount of time given for exposing the recording medium to light, and the amount of light allowed to pass through the lens to expose the recording medium to light. 

A long, long time ago there were various standards for determining the sensitivity of the recording medium, which was glass plates or film.  Over the years new standards were developed, or old standards were modified.  The two “winners” were ASA (American Standards Organization) and DIN (Deutsches Institut für Normung).  Eventually ASA and DIN were morphed together and became ISO (International Standards Organisation).  The values represent the recording medium’s sensitivity; its “speed” meaning how fast it reacts to light.   A film stock with a rating of ISO 100/21° is equivalent to ASA 100 and DIN 21°.  Double the sensitivity of the film and the value would be ISO 200/24°.  Halving the sensitivity would be ISO 50/18°.  With the advent of digital cameras, the sensitivity can be adjusted electronically, and using  the ISO scale.

Now we have to balance exposure time and light to properly expose the recording medium. 

Look at the Exposure Value (EV) chart below,  The first column lists EV values which, essentially, is what the handheld or camera light meter calculated.  Across the top are the standard shutter speeds, and in each of the columns the standard f/stops. 

The aperture is the diameter of the opening of the lens.  Lenses usually have a variable iris to increase or decrease the opening inside the lens.  The aperture is indicated as an f/stop, or f/.  The smaller the value (2.8) more light comes in through the lens.  The larger the number (22), less light passes through the lens.

For example, you have a lens with a focal length of 50mm and it has a 25mm maximum opening inside the lens.  To determine the lens’ “speed” (maximum aperture) you divide the focal length by the largest diameter of the lens.  Using this example the formula is 50/25 = 2, which is a ratio of 2:1 or denoted as f/2. 

If the lens opening of the 50mm lens is 17.8mm, the f/stop would be determined as 50/17.8 = 2.8:1 or f/2.8.

If the lens opening of the 50mm lens is 12.5mm, the f/stop would be determined as 50/12.5 = 4:1 or f/4.

If the lens opening of the 50mm lens is 8.9mm, the f/stop would be determined as 50/8.9 = 5.6:1 or f/5.6.

The “ f/ ” refers to the mathematical function of the lens. 

The term “stop” originated from a time when lenses had no variable iris.  Small metal plates with different sized openings were placed inside the lens via a slot.  The original plates were called Waterhouse (the manufacturer) Stops as they “stopped” (reduced) light reaching the film.

Each time you increase the value of the f/stop by a whole stop, you are reducing the light reaching the recording medium by half.  If you allow more light into the lens by one full f/stop you double the amount of light going through the lens.  The smaller the f/stop number, the more light goes through the lens,  Ergo, f/2 allows more light through the lens than f/16.

Every time you go to a slower shutter speed you increase the amount of light reaching the recording medium by an amount equal to one f/stop.  Going to one shutter speed faster you decrease the amount of light reaching the recording medium or sensor by one f/stop.  Ergo, more light is allowed for an exposure when you go to  slower speed.

An analogy would be a bucket representing sensitivity.  To fill the bucket you have two options: a wide pipe at a moderate rate, or a smaller pipe but at a higher rate.  Using either method stills fill the bucket in the same amount of time.  One balances off the other.

Assuming your light meter (hand held or inside the camera) is set to ISO 125, and it is a cloudy day.  Your meter/camera suggests the setting of f/5.6 at t/1/250 which is an EV value of 13.  On the chart is a horizontal row of f/stop settings in ligher grey.  Any of these f/stops and corresponding shutter speeds will allow exactly the same amount of light to reach your film or digital sensor.  If you want a slower shutter speed, smaller opening (for a narrower depth-of-field), want to catch movement as a blur, or stop action with a faster shutter speed, this chart shows how everything relates, 

Most handheld meters will display an EV setting, and by viewing the dial, or by pushing the meter’s buttons up or down, itwill work just like this chart.  With built-in meters in cameras. the camera’s meter system does all this for you.  The computer inside a digital camera does all this for you depending upon your camera settings.