The Public Shower is, hence its name, a public shower.
The Public Shower is obviously used when a player/mob wants to take a shower. The first example was Herobrine in If Herobrine took a Shower, where Herobrine decides to take a shower for the first time in his life. Another prominent appearance of the shower is in If a Pig took a Shower, where The Pig decides to take a shower because "he smells like Herobrine's Mother's asscrack". However, over time, the looks of the shower changed, from different color patterns, different size and more.
The Public Shower also appeared in "If Minecraft was OUTRAGEOUS" when Steve looks through the walls at a random player showering with a dead bush.