Unless small monkeys try to copulate with orchids, this isn’t an evolved mimicry, but the resemblance is remarkable. Here is Dracula simia from the cloud forests of Ecuador, often called the “monkey orchid” for obvious reasons. But, as I note below, another orchid species is the one that’s most commonly given that name.
Another photo, this one taken by Eric Hunt:
The genus Dracula is quite diverse, with many beautiful species. You can see many of them here. I expect Lou Jost will have a few words about these.
Here’s what is most often meant when someone says “monkey orchid.” It’s the European Orchis simia, which gets its name because the flowers look like groups of dancing monkeys, complete with head, four limbs, and a small tail (e.g., this photo from Wikipedia). It’s said to be “a favorite with children.”
UPDATE: Lou, as expected, has weighed in on the species (see comments), and kindly provided two more pictures of Dracula that he took himself. Here are his comments (flowers in order):
Here are a couple more Dracula pics if you like. The Dracula fuligifera is actually a scan of the flower. It is endemic to my study area near Banos, Ecuador. The other one is also a form endemic to my area near Banos, most like D. exasperata from Colombia but without its hairs. Both occur in EcoMinga’s Rio Zunac Reserve.