What was different about the design of the Globe Theatre compared to modern theatres, and why might it have been built in this way?

Before there were theaters, there were touring acting
companies.  These companies did not have a building in which to perform their plays, so
they toured their regions and played wherever they could rent space.  Most of the time,
that happened to be in the courtyards of inns.  The companies would erect their stage at
one end of the courtyard and the inn's residents would either stand around the stage or
go out on their rooms' balconies and watch from
there.

The Theater was the first permanant theater in
England, and was built by James Burbage.  The shape and form of his theater was taken
directly from the inns in which the acting companies performed.  The Theater was
eventually torn down and The Globe Theater was created from its parts.  The same form
was used, which is why it was shaped in a sort of semi-circle, with tiers of balconies
all around and space in front of the stage in which people could stand to watch the
plays.

Modern stages take a few different forms.  The one
that might closely resemble The Globe Theater would be the thrust stage.  This stage
juts out into the audience, so the audience might be sitting on the three sides
surrounding it.  Another type of stage is the arena stage, in which the stage is in the
middle and the audience sits on all sides of it.  But the most common is the proscenium
stage.  This is what most high school auditoriums have.  There is no outer stage, as in
the thrust and arena types, and a curtain separates it from the audience.  It's like
looking into a picture or a window.

Hope that
helps!