In Shakespeare's time, it was extremely common for an actor to remain with an acting company from his entrance into the profession until his retirement. This could be very helpful for Shakespeare when he was writing the plays because he could already have someone in mind to play the part. The reading gave the example of the character Brutus. It said that Shakespeare probably had Richard Burbage in mind when he designed the role. Richard was an experienced actor and was the "star" of the company so he probably had a strong presence on the stage, which fit the role of Brutus.
This practice makes a lot of sense and I wonder why it's not continued today. Some actors remain with the same company for years, but most of them are performing plays that have been written many years ago. New plays are most likely not written with anyone in mind.
I also thought it was interesting that the company would perform many different plays in succession using the same group of actors. This must have required a lot of work on their behalf and a lot of patience on the directors'. It does make sense though because they would probably be performing for the same people every day and the audience wouldn't want to see the same drama day after day. Doing all the different plays adds variety.