Most photographers believe that larger sensor sizes produce images with shallower depth of field, but that's not exactly true.
Before we can fully explain depth of field, let's talk about how a lens works. Light rays reflect off of an object, and a lens can focus those light rays onto a digital sensor. Focusing a lens will allow a single-point source of light at a precise distance to be focused as a single point on the sensor. Everything else in your scene that is closer or further away from your focus distance will create blur circles on the sensor rather than sharp points because those light rays converge before or after the camera sensor rather than directly on it. These blurry circles are called the circle of confusion and the circle of confusion "limit" is the largest the circle can be while still being perceived as a single point by a human viewer. The further away these rays converge from the sensor, the larger blurry areas of light or "bokeh" will be produced.
What Exactly Is Depth of Field?
Technically speaking, depth of field is determined by what is acceptably sharp by a human viewer, which means that things like resolution, image size, and viewing distance can change the depth of field.
To understand this, imagine that you have a 100-megapixel image file. If you had a 4 x 6 print of this image and you were viewing it at arm's length, you would have a hard time determining exactly what was in focus and what wasn't because the human eye would only be able to perceive about 2 MP worth of detail at this size from this distance. Now imagine you printed the same image the size of a movie screen and could get as close as you wanted to it. From this perspective, you would easily be able to determine what was in focus and what wasn't, which would technically make the depth of field shallower. Camera manufacturers have come up with a standard that assumes that you are going to print the image at an 8x10 inches and view it at 25cm. With these parameters, the circle of confusion limit is .029mm on a 35mm sensor. Anything larger than that will appear blurry.
Remember that a lens is only able to focus on something at one precise distance at a time. Anything closer or farther away from this exact point isn't technically in focus, it just may appear to be in focus to a human based on how much detail they can perceive. If you had a photograph with unlimited resolution and clarity and you could infinitely zoom in without losing any detail, the depth of field would become shallower as you zoom in because you would easily be able to see what was sharp and what wasn't.
Smaller Sensors Usually Produce Shallower Depth of Field
Most photographers assume that smaller sensors will produce a deeper depth of field but technically speaking, smaller sensor cameras usually produce a shallower depth of field because they tend to have higher pixel density/smaller pixels on the sensor. The circles of confusion being projected by the same lens will be the same physical size on both a 35mm and micro four-thirds sensor but when you blow up both images for print, the smaller sensor image will need to be enlarged more to produce the same size print because it came from a smaller source. When you blow it up more than the 35mm image, you are also blowing up everything including the circles of confusion and a human would now be able to more easily see what is in and out of focus.
Remeber how a circle of confusion needed to be less than .029mm to appear "in focus" on a 35mm sensor? On a micro four-thirds sensor a circle of confusion must be smaller than .015mm.
Imagine if you had a full frame 35mm sensor that was 20 MP and a micro four-thirds sensor (which is 1/4 the size) which also had 20 MP. If you attached both cameras to the same 35mm lens, the full frame sensor would capture the entire scene projected by the lens but the micro four-thirds sensor would capture only the center of the scene. Both images have the same resolution but the image taken with the smaller sensor would be zoomed or cropped in and it would give the viewer an even closer look at all of the details. This would allow the viewer to notice details like precise focus more easily meaning that the smaller sensor actually produced shallower depth of field. Check this out for yourself on any depth of field calculator.
In the video above I didn't get too deeply into this because it can get confusing and this phenomenon is very difficult to see unless you have cameras with wildly different sensor sizes and resolutions. The more important bit of information is what exactly is causing changes in depth of field.
The Only Three Things That Affect Depth of Field
1. Changing the focus distance
The only way to change your focus distance is to move your subject or move your camera. As you move your camera further away from your subject, your focusing distance will increase and your depth of field will increase. This occurs because the light rays that are bouncing off of your subject and entering your lens are converging more slowly the further you move the camera away.
2. Changing your focal length
Your lens' focal length is the physical measurement of the distance between where the light rays converge to your camera's sensor. As the lens moves further away from the sensor, the light rays will converge more slowly onto the sensor, which means that light rays will have a tendency to focus further in front of and behind the sensor which creates larger circles of confusion (bokeh) and a shallower depth of field.
3. Changing the lens' aperture
The final way that we can change our DOF is with the lens' aperture. By stopping down the aperture, you are physically blocking the light rays that are coming from the edges of the lens that would produce the most blurry circles of light on the sensor. Closing down the aperture will create a darker overall image, but will also increase the depth of field.
If you'd like an illustrated example of how each of these changes affects depth of field, this video does a great job of explaining it.
The sensor size itself does not produce shallower depth of field, but bigger sensors will force photographers to move closer to their subjects or to use longer lenses to produce similar fields of view of a smaller-sensor camera. Moving forward and increasing your focal length will both decrease depth of field.
If you enjoyed this, you may also enjoy my recent video/post debunking lens compression.