While looking at the resonance form of our Wittig reagent, we see that our carbon has a negative charge while our phosphorus has a positive charge.

Since the carbon has a negative charge, it acts as a nucleophile and will attack our carbonyl carbon.

During the attack, the electrons in the C=O pi bond need to go somewhere. So, the pi bond breaks, and the electrons move to attack the positively charged phosphorus!

From there, we get a cool looking square.

The carbon–oxygen bond will break to form a new oxygen–phosphorus double bond, and the carbon–phosphorus bond will break to form the new carbon–carbon double bond!