Grafting is a method of propagating plants by cloning one plant onto another. This is done to make a new copy of a tree with desirable traits, and is usually done by grafting trees onto a suitable plant of the same genus, called a rootstock. Normally a single bud or a scion (a small section of last year's growth) is grafted onto a rootstock of a similar diameter, but in the case of topworking, scions are grafted onto a much larger branch or trunk of a tree. A great advantage of this grafting method is that the established root system of the tree you graft onto can pump out a lot of growth, meaning the scions will become fruitful trees faster than if you had to start from scratch.
In the above image, a pear tree that had been battling the fungal disease known as pear scab was cut down to about knee height, and two scions of a scab-resistant pear were grafted in place.
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Topworking has a number of uses - for example, if a particular fruit tree is plagued by a common disease you can graft a disease-resistant variety in its place, making use of the mature roots to re-grow a new tree faster than pulling the tree out and planting a new tree. Or perhaps you learned you really don't like the fruits of a certain apple tree, or a feral apple seedling popped up in the edge of your yard - you can switch it over to one or more varieties that you'd enjoy more. Orchardist Eliza Greenman discusses her use of topworking a grove of invasive Callery/ornamental pear into a grove of more ideal pear varieties.
Or perhaps you only have space for one pear tree in your yard, but there are no other pear trees around to cross-pollinate with it in order to get fruit - you can graft a second pear variety onto a primary branch to have two varieties in one tree's location. Sometimes topworking is used by commercial orchardists to turn over an entire orchard row into a more marketable variety; this can be faster and cheaper than pulling out the whole row and replanting.
To see a video demonstration, here is a video of an orchardist with Texas A&M University topworking fairly large trees: Top working larger pecan trees with Dr. Larry Stein.
Above, the same topworked pear tree three weeks later.
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One way topworking differs from other grafting methods is its timing. Whereas a lot of grafting takes place at the end of winter (what's called bench grafting, often using the whip & tongue method) or in August (bud grafting, where you excise a single bud from a scion and insert it into a matching cut on the rootstock), topworking takes place in late spring, once the trees have leafed out and the bark is slipping. It is essential that the tree has fully woken up from spring and the temperatures are warm enough to facilitate a fast healing of the graft.
Otherwise there plenty of similarities. As with bench grafting, the scions must have been collected while they were dormant, and kept dormant in a fridge until they are used - if you tried cutting a fresh branch on a warm day in May and using it as a scion, it already has an active requirement for water, and it wouldn't survive long enough for the graft to heal. Also, good carpentry matters - a simple but skilled cut using a very sharp grafting knife - as does securing and sealing the fresh graft from the elements.
While I pretty much only use bud grafting in my nursery, I think topworking has a variety of valuable applications, especially in and around our neighbourhoods. Did a developer or the city plant an ornamental, inedible pear along a sidewalk? Imagine how much better it would be if you topwork a delicious fresh-eating pear onto it so the neighbourhood has some fresh fruit.
An apple tree randomly grew along the side of your property right next to a road, and the apples are sub-par eating quality and just rot on the ground? You could topwork several delicious varieties onto primary trunks of the tree, turning it into a multi-variety tree that passersby can enjoy. Bought a pawpaw seedling years ago that now has multiple suckers around it that have grown to a respectable size? You could topwork them with improved cultivars so you can experiment with different varieties.
Above, orchardist Cliff England of England's Orchard and Nursery shows off an American persimmon tree years after multiple scions were topworked onto a seedling persimmon tree.
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If you'd like to read more, here is a long article & interview about a cider orchard's use of topworking: Top-Grafting: An Adventure.
And here is a short article and a video from the Philadelphia Orchard Project, which show some examples of topworking in practice: The lost art of yopworking: grafting new fruit varieties on existing trees!