Homolytic bond cleavage is a process where the electron pair comprising a bond is split, causing the bond to break. This is denoted by two single barbed curved arrows pointing away from the bond. The consequence of this process is the retention of a single unpaired electron denoted by a dot on each of the atoms that were formerly joined by a bond. The single electron movement can be denoted by a curved arrow commonly referred to as a fish hook.  These single electron species are known as free radicals. Heat or light are required to provide enough energy for this process to occur.
For example, Ultraviolet light causes the chlorine-chlorine bond to break homolytically. The pair of electrons become split, denoted by the two fish hook arrows between both atoms pointing to both chlorine atoms. After the reaction occurs, it leads to both chlorine molecules left with a single unpaired electron. This is the initiation stage of free radical halogenation.