In the two-part season five premiere, the Cutie Map first appears when all of the Mane Six sit on their thrones in the Castle of Friendship throne room. The thrones react to their cutie marks, and a large crystal table appears in the center of the room, upon which the Cutie Map is holographically projected.
From this point onward, the map summons the Mane Six to other locations in Equestria through their cutie marks to solve friendship problems. Depending upon whom the map summons, their cutie marks glow and pulsate, and holographic images of their cutie marks hover over the location in question on the map. The Cutie Map usually stays visible at all times, but in some episodes it reverts to being just a regular circular table when it is not active.
In this two-parter, all of the Mane Six are summoned to Starlight Glimmer's village to free the ponies living there from her despotic views on equality.
In the two-part season five finale, Starlight Glimmer uses her magic on the map to activate an altered version of Star Swirl the Bearded's time travel spell. In each of the alternate timelines created by Starlight's actions, the Castle of Friendship disappears, but the Cutie Map remains, its landscape changing depending on events that have taken place in that timeline. Twilight deduces that the map remains in each timeline because of its connection to the Tree of Harmony, making it sense that something is wrong.