Yogurt curdles at high temperatures. If you curdle a big lump of yogurt, breaking it up well is hard, and it doesn't taste too well. You want to end up with tiny particles evenly dispersed in the dish. So when you add it a spoon at a time, you can mix it really well before it has had time to curdle.
An alternative method is to do it the other way round. You remove a spoonfull of the curry and dump it into the yogurt, then stir immediately. When it is completely absorbed, you add the next spoon. You continue until you have something like a 1:1 mix in the bowl, then dump it into the still cooking curry and stir.
The second method requires less than 30 s between spoons, but isn't necessarily less work. (You may have to prepare a separate bowl for the yogurt). However, it produces even smoother results. If you have a problematic yogurt (low fat content, high clumping tendency), use the second method.
Edit HenrikSöderlund's comment makes me think that my explanation wasn't clear enough, so here an addition.
The yogurt will curdle a few seconds after it is dumped in the pot. The point is, you don't lumps of curdled yogurt. A lump of curdled yogurt is grainy and sour and doesn't mix well with liquid. Encountering a lump of curdled yogurt in your soup/curry unpleasant in a way similar to encountering a lump of undissolved baking powder in your cake.
On the other hand, A tiny droplet of curdled yogurt is too small to feel as grainy, too small an amount of acid to give you an unpleasant sensation, and small enough to form a suspension with the "broth". That's why you have to break up the yogurt in droplets before it curdles, and this is only physically possible when you start out with a small amount like a single spoon.
It is even more important to do that when adding to the dry-ish mixture described in the edit than when adding to a simmering broth. The broth is below 100°C, the curry base can be much hotter, causing the yogurt to curdle quicker. Also, a liquid will dissolve the yogurt easily and disperse it, but with the dry curry base, you have to rely on stirring only to reduce the yogurt to droplets.