A reducing atmosphere lacks oxygen gas or other oxidizing gases (i.e., lacks gases with a high oxidation state). Unlike Earth's atmosphere, such an atmosphere does not enable oxidation of substances in contact with the atmosphere. It consists of non-oxidizing gases, potentially including reducing gases.
Planets can have reducing atmospheres, and early Earth is theorized to have had such an atmosphere before biological processes produced oxygen. Chemical processes in reducing atmospheres are a potential source of complex organic chemicals, and the theorized early-Earth atmosphere might have been a factor in the development of life. Artificially-created reducing atmospheres are used in some metal processing such as annealing.
An oxidation reduction reaction aka redox reaction is a chemical reaction where one chemical is oxidized, i.e., loses electrons, and another is reduced, i.e., gains the electrons. A chemical that tends to lose electrons (i.e., itself undergoes oxidation and encourages the reduction of another chemical) is called a reducing agent, and if it is a gas, a reducing gas. Conversely, a chemical that tends to gain electrons (i.e., itself undergoes reduction and encourages the oxidation of another chemical) is a oxidizing agent (e.g., oxygen), and if a gas, an oxidizing gas.
The term oxidation was first used for oxygen reacting to other chemicals, but the term came to be used when elements besides oxygen played the role (stealing electrons). The term reduction was first adopted to describe the extraction of pure metal from ores, "reducing" it to the metal by removing oxygen from the compound. A way this was done was with a reducing agent so strong that it first "un-reduces" the metal oxide's oxygen (leaving the metal itself) so the oxygen and reducing agent can carry out their redox reaction.
The term reducing atmosphere is used for atmospheres including reducing gases, such as hydrogen, and can also include gases that are neither reducing nor oxidizing, such as carbon dioxide. The term has also come to include gas mixtures with no reducing gases, as long as no oxidizing gases are present. If an atmosphere were to have both reducing and oxidizing gases, it would be unstable, and inclined to react chemically until one or the other was gone.