A cloak was an article of clothing worn over one's back and shoulders. It could be fastened at the front by ties.
In 2267, Yeoman Tonia Barrows described her attacker as having a cloak and a dagger with jewels on it. Based on her description, Leonard McCoy identified the attacker as Don Juan. (TOS: "Shore Leave")
In 2399, Kestra Troi-Riker wore a hooded cloak as part of her Viveen costume.