Chlorine is the 17th element of the periodic table. In its pure state it's a gas at room temperature and highly reactive–hence very toxic at high concentrations. When combined with potassium bromide, it oxidizes to produce bromine and potassium chloride.
The reaction between pure chlorine (Cl2) and potassium bromide (KBr) is an oxidation-reduction reaction, meaning a reaction in which electrons are transferred or the oxidation number of the participants in the reaction changes. In its pure form, an element always has an oxidation number of 0, so chlorine begins the reaction with an oxidation number of 0. The bromide ion, on the other hand, has taken an electron from potassium and thus has a negative 1 charge, so its oxidation number at the start of the reaction is -1.
Chlorine is more electronegative than bromine, meaning that it has a greater affinity for electrons, so it's able to steal an electron from its less fortunate neighbor or oxidize it. A chlorine that has gained an electron has a negative 1 charge and an oxidation number of -1, so it has become reduced or gained electrons. The bromine, on the other hand, has lost an electron or become oxidized, so it now has an oxidation number of 0. It combines with another bromine atom to form Br2 or bromine gas.
Chlorine and bromine are both halogens, elements under group 17 of the periodic table. As a general rule, each halogen can oxidize the halogens below it in the group. Chlorine, for example, can oxidize bromine or iodine, both of which are below it in the group, while bromine can only oxidize iodine.