On a horse, this is the joint between the cannon bone and the phalanges, or the little projection (with tuft of hair) at the back of this joint. If you're looking at a horse, it's the part you'd probably call the ankle. Of course other animals, such as llamas or even cows, also have fetlocks, but if the word comes up in casual conversation, it's almost certainly in reference to a horse.
The root of the word comes from the Old English fetlak or fitlock, and some dictionaries point from there, to the Icelandic fet, meaning pace or step.
Note - do not confuse the fetlock with the forelock. Trying to show respect and humility towards your ruler by pulling on a fetlock is unlikely to be successful.
The Fetlock in Literature
This may be the only horse joint to be quoted in Shakespeare,
Their wounded steeds
Fret fetlock deep in gore
...which sounds like a bad situation to be in.
Fetlocks also turn up in a bit of Australian verse by CJ Bergerac,
As they drove them up the Barwon
Where the dust lay fetlock deep
And, significantly, mention of the fetlock appears in 'My Lovely Horse', a terrific song composed for the Eurovision Song Contest in the seminal Irish comedy series Father Ted.
Running through the... field
Where are you going
With your fetlocks blowing in the... wind
I want to shower you with sugar lumps
And ride you over... fences