The Book of Esther says, "And he adopted Haddasah, i.e., Esther...and when her mother and father died, Mordechai took her to him as a daughter." (Esther 2)
There are three apparent snags in this verse. First, since the verse says that Mordechai "adopted Haddasah," why does it seem to repeat the fact that he "took her to him as a daughter?" Isn't that the same thing? Second, there is no legal status of "adoptive parent" in Judaism; that is, you raise an orphan girl in your home, but you don't "take her as a daughter." Finally and most notably, "took her to him" is always used in the Torah to refer to marriage.
Literally, then, the verse is saying that he married her.
Why does it use the term "daughter?" The terms "sister" and "daughter" are common expressions of endearment, as we see in other places in the Torah (e.g., Ruth 2:8, Shir Hashirim 4:9) and Talmud (e.g., Shabbat 13b). The idea is that a husband and wife should develop a loving and giving relationship as one naturally has with one's child and sibling.
So, it's not hard to see how the Talmudic Sages saw in this verse support for the oral tradition that says Mordechai, Esther's cousin, was also her husband.