Ok, your curved arrows are weird. Are you showing the triple bond electron pair going to the carbon on the right, like the arrows suggest?
Remember, curved arrows always start AT an electron pair and go TO an electron acceptor. Your second curved arrow is going from the positively charged carbon to the negatively charged oxygen, which is Very Bad. The correct way to draw this would have the arrow going from a lone pair on the oxygen, to the carbon. (Always draw electron pairs in when you're showing a bond forming or breaking, it helps keep you from screwing up.)
Briefly, the alkyne donates an electron pair to the acetic acid, pulling a proton off it. This gives a carbocation and a acetate anion. The anion is a nucleophile, the carbocation is an electrophile, so the anion donates an electron pair to the empty orbital on the carbocation and makes vinyl acetate.