Yevamos Chapter 13, Mishnah 12:
Our Mishnah deals with two separate matters: first, the ruling concerning a minor yavam who performed yibum, and then the claim of a yevamah that no yibum was performed with her at all.
A minor yavam who had relations with a minor yevamah:
The case is that of a minor yavam - below the age of bar mitzvah but above the age of nine, so that halachically his act of relations counts as relations - who had relations with a minor yevamah who is above the age of three, so that from her side as well the act counts as genuine relations. What is their status after such a yibum? Says the Mishnah: "Yigdelu zeh im zeh" - they must grow up together, and if they wish to dissolve the marriage, they will have to wait until they reach adulthood. He cannot give a get until he is bar mitzvah, and she cannot receive a get until she has enough understanding to safeguard the get properly. She need not be fully an adult, but she must reach an age of comprehension.
A minor yavam who had relations with an adult yevamah:
A minor yavam - above the age of nine and below the age of bar mitzvah - who performed yibum with an adult yevamah, who is already past the age of bas mitzvah and mature: "Tigdalenu" - she raises him, meaning they continue living together until he reaches the age of bar mitzvah. If they wish to annul the marriage, he cannot give a get until he reaches the age of bar mitzvah.
The claim of the yevamah that no yibum was performed with her:
From here the Mishnah moves to an entirely different aspect of the situation of yibum: "HaYevamah she'amrah besoch shloshim yom lo niv'alti" - a yevamah who claims, within the first thirty days after the yibum, that although they were together he did not have relations with her and did not perform yibum with her, and therefore she demands chalitzah from him.
Why does she need chalitzah?
The Gemara explains that this is a case in which they can no longer continue living together, because she has already received a get from him, and they are about to dissolve the marriage. For had nothing happened, we would simply tell her: continue living together, and in due time the yibum will take place. Here, however, that is impossible because of the get, and she claims that the get is not sufficient: since she was never had relations with, the yavam never fulfilled the mitzvah of yibum, and he cannot release her with a get alone - chalitzah is required, since that is the way to dissolve a zikah in which no yibum was performed. He, for his part, claims that he did have relations with her and gave her a get, and with that the matter is finished, and he is unwilling to perform chalitzah for her.
In this the Mishnah distinguishes between three situations:
"Besoch shloshim yom" - "kofin oso sheyachlotz lah". We believe her claim that she did not have relations with him, and we compel him to perform chalitzah, since within thirty days it is entirely possible that he did not have relations with her.
"Le'achar shloshim yom" - "mevakshim heimenu sheyachlotz lah". After thirty days we do not fully believe her, since the assumption is that within thirty days he certainly had relations with her, and therefore we do not compel him but only request of him that he perform chalitzah for her.
"Uvizman shehu modeh" - "afilu le'achar shneim asar chodesh kofin oso sheyachlotz lah". If he himself admits, as she says, that he did not have relations with her, then even after twelve months we compel him to perform chalitzah, for the get is not sufficient and chalitzah is required.
In summary: In this Mishnah we learned the ruling concerning a minor yavam who performed yibum - whether with a minor yevamah ("yigdelu zeh im zeh") or with an adult yevamah ("tigdalenu") - that they cannot dissolve the marriage until they reach the age at which a get is possible. We also learned the ruling concerning a yevamah who claims "lo niv'alti" and demands chalitzah: within thirty days we compel him to perform chalitzah, after thirty days we only request it of him, and when he admits her claim - we compel him even after twelve months.