The aperture controls the amount of light entering through the lens. Similar to how the pupil in our eyes can get bigger or smaller to let more or less light in, the aperture can create a wide or small opening to the lens.
Aperture is measured in f-stops, which refers to 'field of view'. This means that as well as letting more or less light enter the camera, the aperture also controls how much detail is in focus: the depth of field.
Depending on the lens you're using, f-stops can range from very wide (large opening) at f1.2, to very narrow (small opening) at f22. But which f-stop should you use, and when?
For landscapes:

A narrow aperture has been used here to ensure a large depth of field.

Notice how the shallow depth of field has blurred the background in this shot.
A higher f-stop number will give you a deeper depth of field, meaning that a lot more detail will be in focus
Better chance of a sharp image
f11-22 are good f-stops to try
For nature photography:

Use of a wide aperture can create a great, blurred background that keeps just your subject in focus.
Can be good to use a wide aperture - f1.2 - f4 - to create bokeh
Keeps focus on the subject rather than surroundings

A narrower aperture (higher f-stop number) will mean that more of your photo is in focus around your subject.
Always good to use a narrow aperture if you want the whole frame to be more in focus
For portraits:
Always remember to have the eyes in focus - where people are first drawn to
Wide aperture can create interesting portraits - especially if close up
f11 good to use when you want whole face to be sharp
For photographing large groups:
Avoid using a wide aperture if you have people in lines in front of one another
Best to use around your lens’s sweet spot - f9-11
The deeper the depth of field (high f-stop number) the larger the area of focus will be in the photo
For night photography:
Use a lens that allows you to have a wide aperture, such as f2.8
See all of our astro and night photography tips
here.
A wider aperture will help light from the stars enter the sensor to create the photo
For animal photography:

An example of using a wide aperture to keep selected detail in focus, and the rest of the image in blur.

Here the photographer has used a narrower aperture to keep more of the image in focus.
For close ups it’s great to use a wide aperture
Create blurred background with a low f-stop number to allow focus to stay on selected detail
If animal is moving quickly, good idea to choose a narrower aperture to increase the chance of capturing a sharp image as it moves through the frame
To create a starburst effect:

Narrow aperture creates a starburst effect on lights.
A narrower aperture will emphasise the rays of light coming from a light source, such as a streetlight.
A wide aperture will do the opposite, and will make the light look soft and blurred.
Read more about aperture here.
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