When a gentleman or lady decides to please themselves via means of intense masturbation or various other forms of sexual stimuli. Not to be confused with milking the cow, no-watering the petunias implies a good deal of artistry involved in the process of satisfying one's desires.
Gentleman 1: Good day to you, sir. You look to be a man about town, as they say, are you not?
Gentleman 2: Indeed I am, but after 9:30 I retire to my chambers to engage in prolonged sessions of watering the petunias.