All the curtains together are known as "soft goods". Individually they have specific names. For this article I am assuming you are in a Proscenium Theater.
Just behind the proscenium wall you will often, but unfortunately not always, find a Fire Curtain. This curtain is made of Asbestos and is designed to fall in case of a fire to prevent fires on stage from spreading into the audience.
The next curtain you will find is a curtain very high up in the air that goes the width of the stage. This curtain is called the Teaser. It is probably the least used curtain in the inventory. It's purpose is to lower down and hide the top of the Grand Drape and all the other curtains that follow. It is used when you want to "lower the trim" of the stage, make the entire stage appear a little shorter.
The main front curtain, which is usually a colored heavy velour curtain, has many names. Some of them are... the Grand Drape, Grand, Main or "Grand Rag". Sometimes the Grand has a valance or short curtain that runs across the top to hide the track. Sometimes the teaser does this job.
Just behind (or occasionally in front) of the Grand Drape you will often find a hard wood flats, covered with fabric. These are called Tormentors, Torms or Hard Torms. They run all the way down to the stage deck. They are typically on a track so that they can easily slide on and off stage. Similar to the teaser, the purpose of the torms is to make the stage smaller... only in this case we are reducing the width of the stage.
Behind the torms you will find a set of curtains that repeats it self several times. First there is a long curtain that hangs high over head and runs the width of the stage. This is a border. It defines the height of the space and hides the lights. Just behind the border you will find a set of legs. A leg is a tall narrow curtain on each side of the stage. These are there to mask entrances and define the width of the stage. Legs and borders are numbered in order starting with the most down stage being 1st Leg or 1st Border. Legs and borders are typically black.
At about center stage there is usually a Mid-Traveler. This is a curtain on a track which opens and closes. At the top it will sometimes have a Valance.
There are several possible curtains you will find at the extreme upstage of the stage. There may be a cyclorama or "cyc" which is a large flat curtain used to project lights on to create scenic effects. Cyc's are typically white but also come in Blue and Gray. You may find a large flat black curtain the width of the stage known as a "back black". You may find an upstage traveler used to hide the cyc or other back drops.
In the wings of a theater farther off stage than the legs you will find a set of curtains that run from front to back perpendicular to the legs. These curtains are called side tabs or "tabs". They are there to ensure the audience can not see back stage.
One more special curtain to consider is a scrim. A scrim is a special piece of fabric sewn more like a mesh or net than a typical fabric. There are hundreds of holes per square foot of scrim. The pattern used creates interesting visual effects. A black scrim when properly lit from the front appears to be a solid curtain. When lit from behind it becomes see through. It isn't 100% opaque or 100% invisible but when properly lit (and with a second curtain that you remove at the last second) this reveal effect can be quite impressive to the audience. A white scrim when placed in front of the action and lit well from behind produces a wonderful dream like effect.