This song, sang primarily by Burr, serves 2 main purposes.
The first is the expression of distaste towards Hamilton. In the previous song, Washington denies Burr a position as his right hand man, and instead invites Hamilton to serve that role. Burr, who has looked down on Hamilton since they first met, became infuriated. This song is the first of many where he expresses his harsh opinions of Hamilton, calling him a "obnoxious, arrogant, loudmouth bother".
The second is the introduction of women in the late 1700s, specifically the Schuyler sisters. Marrying a woman in that time period can hold political importance, as mentioned when Burr said "Looks! Proximity to power". Then came the unofficial introduction of the Schuyler sisters, who possessed both looks and power, by having a very influential and affluent father. Hamilton definitely does not pass on an opportunity to marry one of the sisters, which we will see later in the musical.