The Beatings Will Continue Until
Morale Performance Improves
It does exactly what it says it does. The Drow House Captain can attack an ally with the whip, and that ally gains advantage to attack rolls. The Captain is flogging subordinates in hopes it will make them fight better, and in this case, it actually works. Note that the whip attack does not include the 4d6 of poison damage the scimitar attack has. If the whip was meant to be used on enemies, you can bet a drow would include poison there, too.
It's also different from the Help action, because it doesn't take up the Captain's whole turn - it's part of the Multiattack routine - and can be done from 10 feet away. Sure, it does a little bit of damage, but that strikes me (or the drow's ally, as it were) as a fair trade off for the other advantages it has over Help.
There's at least one WOTC-published hardcover (Waterdeep: Dungeon of the Mad Mage) that features a "whipping chamber" with two drow "engaged in a consensual act of torture" (WOTC's words, not mine). Other scattered references indicate that some drow are just into that kind of thing. Combined with the Drow propensity for slavery, and real-world historical ties between slave driving and whipping, driving people with a whip exemplifies the cruelness of Drow.