a tender way of saying "my dear children," used by a teacher or leader to address the people he loves and cares for as his own family.
This word is the smaller, softer form of the ordinary word for a child, τέκνον. By the time of the New Testament, though, the "little" in such words had mostly worn away. It does not describe anyone's age or size. It is simply a warm word of affection, closer to "my dear ones."
In the New Testament it turns up only as a form of address, always spoken to a group and never as a plain description. Jesus uses it a single time, at the opening of his farewell to the disciples, as a parent speaks to children he is about to leave behind (John 13:33). Every other occurrence is in the first letter of John, where the elder reaches for it again and again to address the community he leads and loves.
The warmth of the word rests on something deeper than the speaker's own feeling. In that same letter, believers are called children of God, born of God. The elder can call them his dear children only because they are first God's children. He speaks as a senior member of the family, not in place of God's fatherhood but within its shelter.