It is combining several similar images into one image. For example to reduce noise one could take 4 similar shots and layer them into one, and the part of noise that is random would be reduced by one half. Or one could take several shots handheld and the slight pixel shifts would be like higher resolution if you follow a certain recipe in photoshop or similar. Or one could have different focuses to make an infocus composite, called focus stacking. I like this website to explain image averaging for noise reduction. https://www.cambridgeincolour.com/tutorials/image-averaging-noise.htm

This is a good description but there is an easier way.
Download digicam control here http://digicamcontrol.com/, free, and load it into a laptop computer.
Mount the camera on a tripod, essential, and tether the camera to the computer. Within digicam set up the near and far focus points and the number of shots to take. Press start and go read a book.
Once finished import the sooc images into Affinity Photo and read some more. Only do your post processing on the final stacked image. Affinity does as good a job of focus stacking as Helicon, zerene and a few others. The two outer images are the result of stacking 60 shots each. The flower is about 6mm high and 12mm deep. D500 + Nikor 105mm f2.8 macro lens. Post in LR and Affinity.

Cindy - Gene's response, thus far - is the most explicit, be it also - the most complicated.

If you have a late model DSLR - including most Sony models, and some of the more recent Canons, and Nikons, you will find you can initiate HDR from the menus. This is a simplified way of doing Focus Stacking, and will allow the camera to do all the work. It will take 3-5 images of the subject, at hand, layering them all on top of each other - to give you the best Photo (with them all compiled) automatically!

It is combining several similar images into one image. For example to reduce noise one could take 4 similar shots and layer them into one, and the part of noise that is random would be reduced by one half. Or one could take several shots handheld and the slight pixel shifts would be like higher resolution if you follow a certain recipe in photoshop or similar. Or one could have different focuses to make an infocus composite, called focus stacking. I like this website to explain image averaging for noise reduction. https://www.cambridgeincolour.com/tutorials/image-averaging-noise.htm

Some photographers will use stacking to achieve depth of field, either in closeup/macro work or landscape. For closeup/macro, you start by picking a picture of something with some depth - like a flower. Using the lens' sharpest aperture, which is usually F8, your first picture will be the part of the flower closest to the camera. It will be extremely sharp and in focus but the rest of the image won't be. If you have a focusing rail, you could then advance the position of the camera forward in tiny increments, stopping to take a picture at each increment. This will move the focus plane deeper into the subject. You repeat this over and over until you are at the back of the flower. You then open a software application like Helicon Focus or Photoshop, and use the stacking instructions to combine the individual images into a single crisply focused single image with what seems completely impossible depth of field for the working distance and aperture. The other, probably more common approach is to simply manually adjust the focus. The problem with this approach is that many lenses made today will have some degree of "focus breathing" which just means that in order to get close to a subject the lens designer changes the focal length of the lens, diminishing it until the minimum focus is arrived at. So in this scenario, the focal length of the first image will be shorter and will lower magnification than the last image. Most software can handle that and make the proper adjustment, but not always.

You can do this and more using smart objects in Photoshop, where you load your individual images as layers and convert them to a single smart object then use a stackmode to do focus stacking, object removal, or noise reduction.

Lastly there is exposure stacking, or High Dynamic Range stacking, where you take a series of bracketed exposures, usually at least 3 and two stops apart, and combine them into a single image using Photoshop, LIghtroom, Photomatix Pro, Aurora HDR, etc. to ensure that you capture detail in the brightest and darkest areas of your scene. Logically, if you can do it in a single exposure it would imply that there is no need to do HDR stacking..

Place the camera on a sturdy tripod – a must!
Frame the subject and compose the shot.
Determine exposure for the scene, and set the camera to manual mode, to ensure that the exposure is constant for every image.
Set the camera to Live View and aim the focus point on the nearest object desired to be in focus. Use the camera’s zoom (+ button, not zoom on the lens) to preview the focus through Live View. Then switch to manual focus and use the focus ring to fine tune for sharpness if necessary.
Take the first exposure.
Without moving the camera or adjusting any settings, move the focus point to an object mid-way in the image and refocus.
Take the second exposure.
Again, without changing anything, refocus on an object at the farthest point of the intended image.
Take the third exposure.
To capture landscapes, three images are generally all that is necessary to create sharp focus stacking images, but it’s completely fine to take extra images to make sure that the entire scenee is covered. A rule of thumb would be to add more images for longer focal lengths. Be aware that extra images will take longer to process in post-production. If available, check the DOF with a Smartphone app, in order to figure out how many images will be necessary, to get every aspect of the photo in focus.
This was taken off the internet.

This is a good description but there is an easier way.
Download digicam control here http://digicamcontrol.com/, free, and load it into a laptop computer.
Mount the camera on a tripod, essential, and tether the camera to the computer. Within digicam set up the near and far focus points and the number of shots to take. Press start and go read a book.
Once finished import the sooc images into Affinity Photo and read some more. Only do your post processing on the final stacked image. Affinity does as good a job of focus stacking as Helicon, zerene and a few others. The two outer images are the result of stacking 60 shots each. The flower is about 6mm high and 12mm deep. D500 + Nikor 105mm f2.8 macro lens. Post in LR and Affinity.