A stadium is the place where football matches take place. Almost every team in the world has its own stadium, where its home matches are played - although some teams share a stadium, such as AC Milan and Inter Milan.
In Football Manager games, the stadium can't really be altered by the manager. All he can do is ask the chairman or board to expand the stadium. This is usually rejected but if the club is constantly getting big crowds at home games and they have plenty of money in the bank, the chairman might agree to an expansion. Sometimes, even when the chairman has agreed to expand the stadium, the local council can deny planning permission. This is because the stadium capacity has reached the expansion capacity value that is set in the database.