It is T-budding and very commonly used in the citrus industry and the stone fruit industry.
The important thing it to do it in the spring when the bark is "slipping". That means that there is active growth of the rootstock/tree, so that the bark is relatively loose (slipping), so that it can be easily peeled back to allow the insertion of the bud in behind bark, where it heals into the cambium of the root stock.
In citrus, for example, you allow 4-6 weeks for the graft union to form, and then you bend (not fold) over the root stock, so that the new grafted but will have apical dominance (it is the highest bud, or close) which will cause the plant energy to be directed to the grafted but. When the new growth is will established, the rootstock growth above the grafted bud is removed.
When the bark is not "slipping" you would use a chip-bud technique, instead.
One of the advantages of budding is that you get more grafts out of the same amount of scion than you would get if you used wedge grafting or which and tongue, etc. In citrus when scion is sold by the bud, you want to maximize your investment by getting a tree from every bud.