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I would like to know the mechanism of this reaction leading to the formation of a geminal dichloride. I am unable to predict how the $\ce{C=O}$ breaks and how the 2 $\ce{Cl}$ atoms replace the oxygen atom. What kind of a reaction is it?
Note: This reaction is mentioned on page 310 of Solomon and Fryhle's Organic Chemistry in the chapter "Alkenes and Alkynes". It's the precursor of the preparation of cyclohexylacetylene through E2 mechanism using 3 equivalents of $\ce{NaNH2}$
I would encourage you to think about how these molecules are likely to interact with each other and try outlining a possible mechanism.
Step 1: The carbonyl oxygen carries a partial negative charge due to its higher electroneegativity. It also has a high affinity towards bonding with the $\text{III}^{\text{rd}}$ row atoms which have $\ce{d}$-orbitals, such as $\ce{Si}$, $\ce{P}$ and $\ce{S}$.
$\ce{PCl5}$ exists as $\ce{[PCl4+][PCl6-]}$. The lone pairs on the oxygen attack the central phosphorus atom.
Step 2: The negatively charged phosphonate complex has high energy (nucleophilic) $\ce{P-Cl}$ bonds. They attack the electrophilic carbonyl carbon. Note that these bonds are more nucleophilic than basic and would prefer substitution over elimination.
Step 3: The lone pairs on the oxygen are next to the $\ce{d}$-orbitals of the phosphorus. They can push out one of the chlorines attached to the phosphorus.
Step 4: The chloride pushes the $\ce{-OPCl3+}$ leaving group out giving the dichloride. As orthocresol pointed out, this step is likely to be an SN1 type of substitution owing to the excellent leaving group and the rather weak nucleophile $\ce{Cl-}$.
Note: Steps do not represent elementary reaction steps. The $\ce{PCl5}$ formed after $\ce{PCl6-}$ gives its $\ce{Cl-}$ is ignored. I have seen/heard Step 3 and Step 4 being described as concerted, but I have shown them here separately as I am not sure of those "rumours".
