If the second metal is more reactive, then it replaces the first metal in its salt. An example below illustrates a typical displacement reaction. Blue copper sulphate solution reacting with solid zinc will give rise to colorless zinc sulphate solution and solid copper. Thus Zn displaces Cu in the salt form. Zn is more reactive than Cu.
Reduction reaction means addition of hydrogen to a reaction.
In a broader perspective, an oxidation reaction is a reaction where an atom or ion looses electrons. Similarly a reduction reaction is a reaction where an atom or an ion gains extra electrons. Oxidizing and reducing agents are those substances or compounds that accept and donate electrons respectively. Example below discusses these concepts in details. Zn itself is getting oxidized.