"Elizabethan plays were being performed in two kinds of theater buildings—later called public and private theaters. Public theaters were larger than private ones and held at least 2,500 people. They were built around a courtyard that had no roof. Public theaters gave performances only during daylight hours because they had no artificial lights. Private theaters were smaller, roofed structures."
So Basically this is saying they had different theater buildings. One that was open roofed, and one that was not. In the public rooms, they gave theaters gave performances only during the daytime. Private theaters were smaller roofed structures.
"The stage of a public theater was a large platform that projected into the pit. This arrangement allowed the audience to watch from the front and sides. The performers, nearly surrounded by spectators, thus had close contact with most of their audience."
This Has inspired many architects. Today, modern theaters like in Las Vegas, have a huge middle platform with audiences surrounding all around.
"Actors entered and left the stage through two or more doorways at the back of the stage. Behind the doorways were tiring (dressing) rooms. At the rear of the stage, there was a curtained discovery space. Scholars disagree about the details of this feature. But the space could be used to “discover”—that is, reveal—one or two characters by opening the curtains."
These rooms helped actors navigate from scene to scene. There were also hidden rooms under the stage for hidden actors for a surprise appearance.