In non-aqueous environments it's pretty straightforward. Oxidation is the reaction in which the metal combines with some other element, oxygen, sulfur, chlorine, etc. and in doing so gives up and electron. Reduction is the same thing in the opposite direction.
The parallel exists in aqueous environments. A metal being corroded, or the site on the surface being attacked, is the anode. The metal is giving up at least an electron and likely going into solution.(if the oxidized species is soluble, corrosion can procede without hindrance of a possibly protective oxide.)
An environment is called oxidizing if the metal either becomes a compound, like Fe3O4, or becomes a cation, Fe+++.
If there is a species in the environment which can reduce the cation, such as chloride ions, which can cause the reaction Fe+++ plus electron = Fe++, the environment can be called reducing, although this is clearly not meant to mean the metal isn't still being corroded. It is a term used to imply that there are competing reactions occuring in a solution. If you add a reducing agent to an oxidizing environment such as Cl- to HNO3, the corrosion rates greatly increases because the reducing ion,the chloride,destabilizes the metal oxide.
Read Chapter 3 in Sedriks' "Corrosion of Stainless Steel.
HNO3 and H2SO4 are considered oxidizing; HCL is considered