"I write unto you, little children, because your sins are forgiven you for his name's sake." (1 John 2:12)
There are two main words for children in the New Testament. One, paidon, refers to little children (as in young). This is the word used by Jesus when he says, "Suffer little children, and forbid them not, to come unto me: for of such is the kingdom of heaven" (Matthew 19:14). Jesus also said (using the same word): "Except ye be converted, and become as little children, ye shall not enter into the kingdom of heaven" (Matthew 18:3).
The other word is teknon, used to designate relationship (i.e. this is my child). John predominantly uses teknon to embrace his relationship with the "sons of God" (1 John 3:2) to whom he is addressing his letter. Although John writes from the perspective of an "elder" (2 John 1; 3 John 1) the "little children" are part of his family in the Lord.
Here in this section of our text, John declares the foundational basis for the relationship with his brothers and sisters in Christ: "because your sins are forgiven" (1 John 2:12). That condition, of course, is what makes us related. John had just exhorted us not to sin (1 John 2:1), but if and when we do, our relationship with the Father provides the Advocate, Jesus Christ.
Yet John also notes (to the believers) that even as "little" (i.e. young) children we had "known the father" (1 John 2:13). Perhaps this is an allusion to the great message writ in the heavens (Psalm 19:1-3) or in the creation itself (Romans 1:20), or perhaps John refers to the foundational knowledge that such children would have heard from their parents. But it surely encompasses the simple truth that God "exists" (Hebrews 11:5) from which all faith must begin. Even little children know that! HMM III