We call an extreme anything that far surpasses the standard or what is rare. Not a little, but a lot. Examples of extremes are:
- Not rather high, but dramatically high.
- Not a little cold, but excessively cold.
- Not some emotion, but abundant emotion.
- Not a bit slanting, but 180 degrees.
- Not some details, but excessive and sharp details on your photo.
The huge London Eye Millennium Wheel
Extremes bring drama or visual impact. They can bring a wow-factor to a photo. They attract attention, so your photo isn’t overlooked easily. And that is an important start for a good and interesting photo.
Extremes are related to what we called oddities. 
As opposed to extremes, oddities are only uncommon, or slightly uncommon. An oddity will become simply weird or bizarre when taken to the extreme. Also, extremes don’t have to be an oddity. That fire is hot is not strange and well-known, it’s no oddity. But the very high temperature can be called an extreme.
Now the concept what you can pursue is clear, it should be said there are limits. Standing on the top of the Mount Everest is probably an extreme, but likely you won’t climb it every year.
Hunting to photograph a near extinct bird is not advisable and must be discouraged. But capturing a beautiful, but not so common bird with all the details remarkably visible, will get warm attention.
It about the mixture of ingredients that makes the photo. Having a photo with not so excessive extremes, but with great lighting, composition and story will make a lasting classic, worthwhile photo.
You can see examples of extremes on our examples page, and at the bottom of the ‘tips per subject’ pages:
Landscape photography tips
Baby photography tips
Aerial photography tips