Dayan asked me what that meant. I said, 'he likes his style/how he operates.' Which was correct. But I incorrectly added that I *thought* a jib was an article of clothing. Since I was on the laptop I decided to google it because I really didn't know what a jib was.
Turns out a jib is one of the triangular sails on a ship, and that different nationalities of ships had different styles of jibs. They were easily identifiable from afar, which allowed sailors to make their judgement on the approaching ship. Hence the phrase being about liking what you see of a person's appearance or character.
Edited to add: check out the comments, where Meljean Brooks has provided a more complete explanation.
I came across this cool post on vintage menswear while googling:
I Like the Cut of Your Jib, Sir.."

VJ says: Those are some boney-assed manorexic knees, young Charlton Heston and Spencer Tracy.
Another link I found said the turn of speech didn't enter the popular lexicon until:
The phrase became used in an idiomatic way during the 19th century. Sir Walter Scott used to it in St. Ronan's Well, 1824:
"If she disliked what the sailor calls the cut of their jib."
There may be an allusion between the triangular shape of noses and jibs in the figurative use of this phrase, but this isn't authenticated.
Hmmm... is it me. or does that comment about noses hint at the possible anti-Semitic sentiments of times past?
Moving along, here's where things get ridiculous. I thought the Sir Walter Scott reference was a bit of a vague jump-off point for the phrase to enter mainstream language/slang and decided to dig further. Enter the Yahoo! Answers message boards.
The question posted two years ago on the board was this:
"If someone tells you that they 'like the cut of your jib,' what does it mean?
A guy told me this in an email and I don't know how to respond."
This was one of the answers:
well, basically, he, means, that, he, likes, the, way, you, cut, your, jib. some, people, stay, up, all, night, cutting, their, jib, but, not, you, your, jib, is, already, cut. Either, that, or, he, wants, you, to, cut, your, jib, in, front, of, him.
Source(s): School of Jibs.

LMAO!
And here's another answer:
he can see the outline of your patch or slit. which means you should start wearing panties and your jeans are too tight.

errr...... so, yeah....
Do your googling with care and common sense boys and girls.