As a human pony, I do not mind (and often enjoy) having a twitch applied to me on some occasions. However, I am not a fan of these applied to my bio-equines even though they are supposedly humane and not applied with the intention of inflicting pain on bio-equines (you can see the Wikipedia article here for an explanation of how it works on a bio-horse without causing pain).
A twitch is used to distract and restrain a pony. The loop of chain is applied (most often) to the upper lip and the handle is twisted until the loop of chain becomes tight. This is most often done to allow veterinary procedures to be performed on the pony.
There is also a "pincer" type twitch, which works similarly by squeezing the upper lip, but instead of twisting a chain to get a tight fit, you simply squeeze on the handles. This type of twitch does not usually fit a human pony's upper lip, so keep this in mind if you are thinking about purchasing this type of twitch from a bio-equine tack store or online retailer.