The world of theatre, like any industry or "organised activity", has it's own terminology and definitions, more commonly referred to as "Jargon". Here's a few of them...
Proscenium Arch (or Pro Arch)
This is the "frame" of the stage, going up the sides and across the top of the stage opening.
Flats
Simply, large wooden or metal frames with either canvas stretched over them or clad with hardboard. On to these are painted the scene back drops, such as a countryside scene or a city skyline.
The Set
This is the setting of the play, it may be a living room, an office or anywhere that the action could be required to take place. Some productions require more than one location, which means either having all the sets on stage together or changing the set during a "scene change".
Fly-In, Fly-Out, The Fly Tower
If you've ever been to the theatre or seen a variety performance on T.V., then you may have noticed scenery, pieces of set or flats dropping in from above. This is known as "flying"...
If you fly-in, then a piece of set or scenery is dropped on to the stage and in to view for the upcoming scene. If you fly-out, then a piece of set or scenery is lifted off the stage and out of view. In most purpose built theatres, this scenery resides above the stage in what's known as the "fly tower". You may have noticed the area above the stage is usually the tallest part of a theatre building.
Indeed, to accommodate the scenery, which is normally from the stage floor to the top of the pro arch in height (at least), the fly tower has to be more than twice that height.
Sometimes, sets and flats are not the only things to "fly": actors (or their stand-ins) are required to fly the set. If you've seen a big theatrical production of "Peter Pan", then you will have more than likely witnessed this.
Blocking
When characters enter or exit the stage or move around the set to any degree, this is known as "blocking". Not only are the actors required to learn and rehearse the lines, but also to learn their blocking, every movement around the stage made by the actors is worked out and rehearsed in advance to ensure the action of the scene moves smoothly.
For example, if a character is required to be shocked by something they see or hear, it would be natural for them to stand up suddenly (if sitting down) or move backwards (if already standing) in response. When the character does this, you may need anyone standing behind them to move, so they are still visible to the audience. All of these things needs to be taken in to consideration and allowed for during rehearsals.
Choreography
Whether it's a dance number or a fight, it all needs to be choreographed so that everything happens in time and contributes to the content and look of the scene. In addition to this there is a safety issue: if you have actors performing complex sequences while moving quickly, you don't want them to connect with each other as this could result in an injury. This is particularly true for fight scenes, even though the protagonists will have to appear to be hitting each other!
Stage Left, Right & Up Stage, Down Stage
When a scene is blocked, any instructions given by the director are from the point of view of the actor. So, when the actor moves to their left, that is "stage left". From the point of view of the audience in the auditorium, they are moving to the right. The reverse is true for stage right.
In a theatre, so that the audience can see all of the action, the stage is on a slight tilt or "rake", with the rear of the stage being higher than the front. When an actor moves to the rear of the stage, they are said to move "upstage", where they can be seen by more of the audience. This is where the saying "upstaging someone" comes from.
The Wings
These are basically the areas off to the sides of the stage out of sight of the audience. This where actors await there cues to enter (hence the term "waiting in the wings") and/or where items of the set, scenery and props are kept.
The Scene Dock
This is a loading and unloading bay usually located behind the stage or in the wings. As the name suggests, it's primary use is for the unloading and loading of scenery and sets.
The Safety (or Fire) Curtain
A fire proof curtain that drops down in front of the main stage area to isolate the audience in the event of a fire. Regulations dictate that the safety curtain must be dropped in the presence of the audience. This usually happens in the interval, it can then be retracted for the rest of the performance.