Those conditions refer to different methods of carrying a single action type semi-auto pistol, like the Model 1911 and its clones.
Condition 1 is magazine loaded, chamber loaded, hammer cocked, and safety on. This is the recommended carry for any immediate use.
Condition 2 is magazine loaded and chamber loaded, but with the hammer down (the safety can't be set with the hammer down). This is a little more dangerous if the gun is dropped, and necessitates cocking the hammer before the gun can be fired.
Condition 3 is with a loaded magazine, but with the chamber empty and the hammer down. This is the mandatory way of carrying in the military, and necessitates "racking" the slide to chamber a round before the gun can be fired.
Sometimes there is mention of Condition 0, which is chamber loaded, hammer cocked, and safety off - in other words, ready to fire.
Some people add a Condition 4, which is with the magazine empty or removed, the chamber empty, and the gun stored or ready for storage.
Others have added other "conditions", such as Condition 18, which is in the hand of your wife who has just compared notes with your girlfriend in the ladies room, and Condition 23, which is at home in the desk drawer when you are carjacked. Neither is recommended.
Jim