For the full harmonious development of his or her personality, the child should grow up in a family environment in an atmosphere of happiness, love and understanding. (Preamble to 1989 United Nations Convention on the Rights of the Child).

For many children, for one reason or another, they are unable to live with their biological parents. One of the key principles for undertaking intercountry adoptions stipulated within international conventions is the principle of subsidiarity.

The principle of subsidiarity requires that the priority wherever possible is for the child to grow up with their biological family. If this is not possible then a domestic family-type solution must be actively (and genuinely) sought.

Intercountry adoption should only take place if a suitable domestic solution cannot be found for the child. It is important to note that the overriding principle of all adoptions must be the best interests of the child.

Therefore there may be situation where it is in the best interests of the child to be adopted into another country (e.g. relatives living abroad) when suitable domestic solutions exist.
(Reference: International Social Service)

One simple way to easily understand the the principle of subsidiarity. Imagine the following dialogue:

The novice:  But why is it so complicated to adopt a child when it seems that the world is overwhelmed with children in need?

The expert: It is important to firstly ask whether the children are adoptable, that is ensure that the possibility of relying upon alternative care measures in their country do not exist. To illustrate this, imagine you have two children and you die in a car accident? What would you want for your children?

The novice: It would be normal that they stayed with their mother.

The expert: Of course. And if the mother also died during the accident?

The novice: In that case, I would like the children to be placed in the care of our family: the grand parents, or uncles or aunties for example. 

The expert: That's right. And what if the family cannot look after the children, either because they do not exist or do not have sufficient resources? 

The novice: In that case, I would like my children to grow up in their country, in a framework more or less familiar, where they can pursue their schooling in their mother tongue etc.

The expert: And now you see, it is the same thing for all the parents in the world that international adoption should only be considered after all the options that you elaborated upon before are not possible. That is the principle of subsidiarity.