Answer
This is a redox reaction. Mg acts as a reducing agent and $Br_{2}$ acts an oxidizing agent.
Work Step by Step
In a redox reaction, there is a change in oxidation number.
Mg's oxidation number changes from 0 to +2. Since there is an increase in its oxidation number, it gets oxidized. Hence, it acts as a reducing agent.
$Br_{2}$'s oxidation number changes from 0 to +2. Since, there is a decrease in oxidation number, it gets reduced. Hence, it acts as an oxidizing agent.