The phrase “cut of your jib” is an idiom that refers to a person’s general appearance, manner, mien, style, demeanor, or personality. It is usually used in the phrase “like the cut of one’s jib”. The phrase comes from the jib sails of a boat, which denoted a ship’s allegiance and potential hostility. If someone likes the cut of your jib, they will forgive you the odd lapse.
For example, you can say “I like the cut of your jib” to someone who has impressed you with their attitude or behavior. Or you can say “I don’t like the cut of his jib” to someone who has annoyed you or rubbed you the wrong way.
The origin of the phrase is nautical. The jib of a sailing ship is a triangular sail set between the fore-topmast head and the jib boom. Some ships had more than one jib sail. Each country had its own style of sail and so the nationality of a sailing ship, and a sailor’s consequent opinion of it, could be determined from the jib. The phrase was being used figuratively by the early 1800s, often to express like or dislike for someone.