The stage sets can help set a scene and make a show more realistic. A set can make the scenes feel better and make a scene make more sense. For example, if there is a party scene in a play if they put a party room backdrop and some decorations to fit the mood. If it is a city street late at night. They can put out lampposts, a city like backdrop and dark lighting.
When it comes to sets there are many involved. The makers of the set who make the backdrops, constructed set pieces, and make the special embellishments, there's the set designer who designs the set with the director. There are also the people of stage crew who are in charge of the set while the show is going on and pulling ropes and wires to get the sets on and off.
There are many types of set pieces and ways the work, backdrops are usually symbols of were a scene in the show is taking place (ex. home, street, office etc.). These usually are pulled and changed from ropes backstage. There are also objects like furniture, doors, and landscape (fake trees or bushes etc.). These are ether pulled on and off stage manually by stage crew, some can enter and exit the stage on tracks they are attached to and wires pulled by someone backstage. Many professional theaters and shows have motorized sets that can go and leave the stage without anything attached usually powers by a remote control. Most of the time set pieces are moved during a blackout (when they turn off all the lights and the stage goes black, usually to transition to the following scene)
Sets are a big part of the show, without them audiences can't feel like they are in the world of the show and they lit up the stage and make it more decorative.