What is the reaction which converts alcohols to halogenoalkanes called?

Halogenation of ethanol to form chloroethane is a nucleophilic substitution, type SN2.  
SN2 is also called "bimolecular" nucleophilic substitution - nucleophile's lone electron pair attacks an electrophilic centre (electrophilic = electron deficient, therefore "electron liking") and forms a bonds with it.  When that happens, the "leaving group" is pushed out, so incoming group replaces the leaving group in one step.  In this case, the "incoming group" is not a group, just an atom (Cl), and the leaving group is hydoxyl (-OH).

The other type of nucleophilic substitution is SN1, which is a unimolecular nucleophilic substitution involving a reactive intermediate (carbonium ion) and is seen in the formation of secondary or tertiary haloalkanes tertiary alcohols.