One use for a scrim is to create a dark, shadowed effect. Place your actors behind the scrim but in front of some sort of light source. A scrim, when lit from the front, appears opaque, allowing it to be a wall or a divider for whatever the set calls for. When lit from behind with varying levels of light, a scrim can allow anything from shadows to display on the scrim to near total translucency. Using a small amount of light from behind can give you a very useful shadowy silhouette effect to allow more risque (or impossible) things to appear to happen on stage.
A scrim used as a background has the added ability to be used dynamically. A scrim, by nature, appears white to the audience though it is actually a more reflective material. This means any color shot on the scrim will make the entire scrim appear to be that color. Shooting any combination of lights with colored gels over them onto the scrim allows you to create a mood and atmosphere dynamically within your play, just as you would with regular lighting.
When shot with light from the front, a scrim acts as a completely opaque barrier that actors can then use as additional entrance and exit points at the director's discretion. It also gives the illusion of additional depth as people move past the scrim to exit or utilize the space behind it. All of this can be applied to your blocking to give more choice and create a more believable space for your actors to interact in.
A scrim can utilize both front lighting and back lighting to create dynamic settings that can change the scene without a set change. Place the first scene in front of the scrim with light coming to the front of the scrim, making it opaque. When the scene calls for the dynamic shift, change the lighting so it is lit from behind, opening up a large section of the stage the audience was not able to see before, displaying your new scene without changing the set.