If we say that someone or something has been adopted, we can be conveying a number of different meanings, depending on the context.
The roots of the word "adopt" means to choose, and most uses of the word will convey that sense of choice in one form or another. If we say that someone has adopted a child we're referring to the fact that they have taken a child of other biological parents as their own. Usually this is a legal relationship, though many people will describe a child with whom they share a strong bond as being informally adopted - that is, a child of their heart, if not of the law.
It's not only children who can be adopted. Lawmakers adopt bills into law - that is, they are formally accepted, passed, and put into effect. Highways can also be adopted when a group or business assumes responsibility for cleaning and maintaining a particular section. And when you say you've adopted an idea or a cause, it means that you have embraced it as your own.
In most cases, when we use the word adopted we're referring to the process by which the biological child of one family becomes the legal and/or emotional child of another. Sometimes the individuals involved may be biologically related, as when a grandparent adopts the children of his/her deceased or incapable son or daughter. Other times the relationship may be the outgrowth of another, as with a stepfather who adopts his wife's biological children. In still other cases there may be no connection at all until parent and child meet, such as a husband and wife who travel to China to adopt a daughter. In all these instances, the child is adopted - chosen - taken as one's own, into both the home and the heart.