One of the things I want to achieve in my photography is bokeh (blurry background). The things that affect this, according to the Internet, are sensor size, aperture (f numbers), and distance.
Now, I realise that DSLRs will give you much more bokeh than any compact camera (with the possible exception of the full-frame Sony RX1 which costs about £2700 and I'm not paying anywhere near that), but I find that I can get good bokeh with my new Sony RX100ii sometimes. Of course, I wanted to find out why I was getting better bokeh at sometimes than others. I knew it had to do with aperture (how much the camera squints), and distance from the camera. Last night the phrase "depth of field" finally hit home and I realised that it's about relativity.
To demonstrate for yourself how depth of field affects bokeh, hold out your index finger in front of you and focus on it as you move it towards an object that's in front of you, and then towards your eyes. As you move your finger towards the object, the object will come more into focus, and as you move your finger closer to your eyes, the object will get blurrier (that's bokeh).
This is what happens in photography. The better your sensor and lens, the more pronounced these effects will be because your camera has better eyesight. If you try the above experiment while squinting, you'll see what a difference quality of camera and lens makes.
The bigger your subject, the greater the distance will have to be between it and the background because the camera must be farther away from the subject to get the whole thing in the frame. The reverse is true as well: macro shots have great bokeh because there is very shallow depth of field, i.e. the subject is close the camera, so the background is far away compared with this distance.
I think there must be a ratio for this, but it will vary from camera to camera. I think on mine, the distance from the subject to the background must be at least four times the distance from the subject to the camera to get good bokeh.
Here are some images that demonstrate the idea, and that I took last night when I was figuring bokeh and DOF out:
Above you can see how the closer the usb stick is to the camera, the blurrier the tissue gets.
Above, you can just see how the closet I am to the camera, the blurrier the printer and books are. It's not as pronounced in these images because the distance isn't very big compared with me.
It also helps if the background has bright lighting with different colours, like if you're standing in front of a backlit tree or some fairy lights. You'll have to Google image for that though.
I'll add more about photography as I learn it and actually understand it, but I can't say that will happen very regularly! : )