While no expert, I believe the joke is that 4:20 is the time* at which a lot of people partake in smoking marijuana, known on the street by many names, particularly "weed". The gif says in the box "You can now identify weed", presumably with the first part of the plant edited out. As the player of the game can now identify the narcotic drug he can now join in with 420 and smoke some marijuana. However, I think that the main joke is actually pointing fun at the entire culture of 420 and how idiotic it can make people look.
*I think this is where is came from, but I do know for definite that many people smoke this stuff heavily on 20th March, or 4/20 in the bizarre American date system.
