I assume that you are asking about factors that determine whether human beings decide to domesticate certain plants and animals. Jared Diamond has discussed this topic at length in his book Guns, Germs, and Steel. I will base my answer on that book.
Essentially, people decide whether to domesticate a plant based on how useful the plant would be to them. On p. 119, Diamond lists some things that would make a plant useful. Some characteristics include:
- Big edible parts (fruits or seeds)
- Fruits that have a high ratio of flesh to seeds
- Nuts that are oily
- Plants with long fibers, like cotton, that can be used for clothing
All of these are characteristics that humans would have noticed. They would have chosen the plants that had these qualities and domesticated them.
Diamond devotes all of Chapter 9 of his book to discussing why some animals are domesticated and others are not. Basically, the answer boils down to whether it would be valuable and safe to domesticate the animals. Some specific characteristics of animals that can be domesticated are:
- Herbivorous. Carnivorous animals are too hard to feed.
- Grow quickly. If the animal grows too slowly, you have to feed it for a long time before it is useful.
- Will breed in captivity.
- Have a good disposition. Fierce animals are dangerous to domesticate.
- Do not tend to panic. Animals that panic and stampede easily are not good to domesticate.
- They have to live in herds and not be too territorial.
These characteristics would have allowed people to domesticate certain animals. They would have picked those animals with these characteristics to domesticate.