This is Kidushei Kesef (money), which is one of the three forms of Kidushin mentioned in the Mishnah (2a). In this case, however, the Gemara explains that this Kidushin takes effect through a combination of the precedents of the law of "Arev" and the law of "Eved Kena'ani."

1. The Arev is the guarantor for a loan who becomes obligated to repay the loan if the borrower is unable to do so. Even though the Arev received no monetary benefit in return for his obligation, he obligates himself; the pleasure he receives from the fact that the lender lent money to the borrower based on the Arev's word is enough for him to obligate himself. Similarly, a woman can become betrothed even though she receives no monetary benefit, but instead she receives the benefit of the man listening to her directive and giving the money to someone else.

2. The Eved Kena'ani is the Nochri slave who is set free when others give money to obtain his release. This law teaches that a person can acquire his own freedom even though he gave up none of his own money to do so. Similarly, a man can acquire a wife even though he gave up none of his own money to do so.

When the woman says to a man, "Give this Maneh to so-and-so and through this I will be Mekudeshes to him," this is a combination of processes (1) and (2). The woman received no monetary gain, and even so she gives herself over to her husband, as in the case of the Arev (1). Moreover, the husband acquires a wife even though he did not spend anything, as in the case of the Eved Kena'ani (2).

Kol Tuv,

Dovid Bloom