Mishnah 11 in chapter 13 of Maseches Yevamos opens with the phrase "Gedolah u'ketanah": a man who was married to two women - one of them an adult, a girl who had passed the age of mitzvos, and the other a minor, who had not yet reached that age - and he died. The Mishnah discusses two possible orders in which the yibum could be performed, and the halachic result that follows from each one.
The first case - the yavam first came to the adult:
If the yavam performed yibum with the adult and came to her, and afterwards came to the minor as well, or his brother came to the minor - since he too was fit to perform yibum - "Lo pasal es hagedolah" - he has not disqualified the adult. The yibum with the adult was a complete yibum and took effect, and whatever happened afterwards is nothing more than a legitimate relationship.
The second case - the yavam first came to the minor:
If the yavam performed yibum with the minor first, and afterwards came to the adult as well, or his brother came to the adult, "Pasal es haketanah" - he has disqualified the minor. The reason lies in the difference between the two:
The minor: her obligation of yibum is based only on a marriage that is rabbinic, while on the Torah level there is no marriage here at all.
The adult: her marriage, the bond created toward her upon her husband's death, and likewise the yibum performed with her - all of these take effect on the Torah level.
Therefore the relations with the adult disqualify the minor, since the minor's yibum is only rabbinic.
The opinion of Rabbi Elazar:
Rabbi Elazar says that in such a case "Melamdin es haketanah shetema'en bo" - we instruct the minor to perform mi'un, and through this she annuls the bond that was created between herself and the yavam, and the adult is released from the first yibum that was performed with the minor.
Why is this advice needed? Because if she does not do so, not only is the minor disqualified, but the yavam cannot remain married to the adult either: after all, a yibum has already been performed, even if only on the rabbinic level, and a man does not perform yibum with two yevamos from one household. It turns out that the adult is disqualified as well, since her relations were second. For this reason Rabbi Elazar ruled that the best course is to instruct the minor to perform mi'un, and in this way the one who performed yibum with the adult can remain married to her.
In summary: in this Mishnah we learned that performing yibum with the adult first does not disqualify her, since her yibum takes effect on the Torah level; whereas performing yibum with the minor first, which is only rabbinic, is undone by the relations with the adult that follow. Rabbi Elazar shows the way out of the deadlock - the minor's mi'un, which allows the yavam to remain married to the adult.