This action has something to do with the achievement: Unlife is Strange. You can find the flower in Jonathan Reid's office, on the first floor of Pembroke Hospital. When you interact with the flower, your character will state, that the flower will wither without water. However there's one issue - There is no place you can purchase it, even in Whitechapel.
To water the flower, you need to visit West End. This is the last district, you'll visit in the game. You won't be able to arrive there until you reach the 4th chapter of the game - when Jonathan will be on about 20th experience level. You can get water only in the second half of the game- so don't worry, that you have missed something.
Don't worry about the fact, that the flower, withers, because there is no option, that your plant would die permanently. When you get water, you'll be able to return to the Pembroke Hospital and after that, water the flower. After that you will gain achievement called: "Unlife is Strange" Just remember, time is what the flower needs to bloom again. In this game it takes some time, and it'll be necessary to wait a few nights, awaiting the results of your efforts.