"3 glasses of cognac" (type of brandy)
Joke is about formal/polite vs informal talk. 'Ты' is informal 'you' and 'Вы' is polite/formal 'you'. So, 'перейти на ты' is about switching from formal/polite style of communication (Glad to meet you, mr. Johnson!) to informal one (Wazzzaup, buddy!).
Joke is built around play of words with similar "...goes to..." related to different processes.