What does the quote "you become responsible, forever, for what you have tamed" mean?

Means that we must correspond the feelings we are putting in some relation.

Explanation:

Tamed means to touch someones heart, to know them, this gets vulnerability appear and then you must be responsible for that, continuing building the relation with the same respect at the beginning.

The quote "you become responsible, forever, for what you have tamed" was taken from the book The Little Prince, by the author Antoine de Saint-Exupéry.

One character, the fox, tells the main character of the book, the Little Prince, that he is forever responsible for someone whose life he has touched and somehow changed. In this context, the verb "tame" means conquering someone's heart, little by little.

Overall, the quote means we should always be kind and thoughtful towards others, never taking their love and affection for granted, being considerate of their feelings and emotions.