What is high-yield farming and why is it a solution for deforestation?

The limited answer is that if you increase yields per acre somehow that means less native forest will succumb to the plow. I don't really agree with that, from another view that means you get more profit per acre, so, buy more acres to profit from is what'll happen. To maintain yields without adding costly amendments like fertilizers and pesticides is more the goal as most farmers a decade or more ago came to the reality of exponentially increasing costs in financing the next year's crop and machinery along with the fuel to harvest and plow that dirt, so, they backed off the standard routine and began less costly ways of attaining the same yields as before. Now that means you track areas of your land that need special care and get to it, if one section gets less soil moisture people put up snow fences to drift in more snow as an example. The big agribusinesses will get there as well, the price of fuel keeps going up, that means you plow less and save it for harvest. No-till is hot, plowing is not. Organic farming has it's pluses, one of them is that your amendments are usually cheaper along with less pesticide use in general such that costs can be less than standard farming practice, but it takes more knowledge and skill in organic methods than is easy to learn and apply to your particular farm, soil and weather than regular farming, harder to do at that level. Seed companies do keep coming up with better yields, pest resistance and so on, but they are patented and so very expensive to use for the average farm, you've seen the lawsuits by the big seed business over a farmer whose land had been polluted by these patented seeds from an adjoining farm. He fought back and won but that's pretty telling on what happens and why most smaller farms avoid them and now prefer to raise, prepare and store their own seed whenever possible. As for preserving forest, that's also done more by smaller farms ... so if you want to preserve trees, then preserve small farms.

Generally high yielding farming in your question needs to be clarified. There are two ways of looking at the situation. The first is that we can improve production in low or poor performing regions of the world. The second is a focus on improving production in already productive areas. Now if you take the later, you can improve the production of marginal lands which are already cleared, you have a huge potenital to reduce the need for more land to increase production. And interestingly, these areas with poor performing lands generally tend to be in third world countries - thus increasing production reduce the need to clear trees.

its cutting down every tree burning it them planting crops in the ashs so that it grows and we can eat it then we burn the plants and grow more

High yielding isn't any one specific method. Maximizing the number of plants in a given space is a high-yield method. Certain varieties or breeds of each crop and species of livestock are considered high-yield becuase they produce comparatively more food. In theory, increasing yield could potentially reduce the amount of space required to farm and thus the less land that has to be cleared for farming. The problem is, individual farmers will not likely stop increasing their fields becuase of this. If they can still get a good price for their crops locally or somewhere they can ship to, expanding their farmland will be more valuable with high-yield farming than other methods. Expansion of farmland really depends more on international markets (costs of production and prices at sale) for each product than the yield of a farmer's fields.