He served in the British 7th Armoured Division under the command of Captain Price, seeing action in El Alamein, Tunisia, and even as far as El Daba, Egypt. He then fought in the liberation of Caen just after the events of D-Day.
An example of a player-character speaking in-game, but being unheard by the player, can be found in the mission "Operation Supercharge". When the player has finished clearing the final house, Captain Price will order Davis to find a radio and tell HQ and that they secured the rally point. When he does this, the soldier on the other end will praise him for his good work, despite Davis seemingly having said nothing.
In the mission "Prisoners of War", after the player finds the wounded Americans, Captain Price will order the player and MacGregor to bring back the truck to transport them. When he does this, he addresses Sergeant Davis as "Corporal Davis". This is the only occasion in which he does this. It is possible that Davis was originally going to be a Corporal in the game, or it could simply be a mistake on the developers part.
John Davis seems to be second in command of his squad. However in El Daba, he is third in command because of Cpt. Burwell.